Can a Drill sergeant search you and only you without permission?

So, what you're saying is that your DS caught you doing what you weren't supposed to do, apparently more than once based on your comment about not being used to the freedom? On top of that, you believe that your DS is like a police officer who can only search her barracks (the ones you're staying in, and she's responsible for keeping safe and clean) when there's legal probable cause?
It sounds like you've been talking to the barracks lawyers too much.
You got caught doing what you weren't supposed to do. Then you made yourself a target and confirmed your DS' suspicions by becoming a repeat offender. All you've managed to do is confirm to your leadership that you are not capable of maintaining the same level of discipline and standards as your peers. There's an old saying in the Army, "90% of your time is taken up by dealing with 10% of your Soldiers". You've identified yourself early on as the repeat offender 10%.

If you can't take it, feel free to go talk to the 1SG. Tell them how you did, in fact break the rules, but it's not fair that you were targeted because.... Reasons.... I'm sure that 1SG will condone your actions with a complimentary Article 15 so that you feel more fairly treated.

Also, you're writing in English, your job will soon be to write memos and correspondence to commanders, XOs, and other officers. Learn how to use punctuation and write correctly.

I'm going to go with the premise that you are a young troop, new to the Army, looking for legitimate advice and not sharpshooting from the internet mob.
If you think you were done wrong in this situation, there is a chain-of-command for that. There are also outside CoC forms of redress, such as the IG, but I would caution you to use the CoC first.
Yes, by regulation the DS can toss your locker. He/she does not need probable cause, as your living space and everything in it are inspectable items at any time. Not that it matters, since the DI DID have probable cause since you had previous infractions. Turns out, their suspicions were correct. You might want to ask yourself how the DS found out about you having a phone. Hint: not everyone in your platoon likes you.
Having said that...
If you can't take it for two months, the Army is not for you. We tell you to do things you don't want to do; even dangerous things that might cause you bodily harm or death. We have rules you are expected to follow, and if you don't your property might get confiscated. You might even find yourself getting called on the carpet to explain yourself, but not really since it is a one way conversation, where an authority figure will chew you out for not following orders and take away your money, your rank, maybe even your job.

Look. I have been doing this for 26 years, and I figured a couple things out. If you show up in my formation, I don't know you from Adam at first, except insofar as you get there on time and in the right uniform. Troops on the radar are there because they did something to get on the radar. Do what you are told, get there on time, and be ready to train and we will get along smashingly. Get in my crosshairs by doing the wrong thing, try to barracks lawyer me, and break rules blatantly and repeatedly and we will not get along. It will go poorly for you, because I have lots of stripes and you do not.
It has nothing to do with "liking" you or not. It has everything to do with are you a disciplined member of a team that I can depend upon in combat or not.

My advice is simple. Shut up, ruck up, and follow the rules. You only have to manage that for two more months and you graduate and move on in your Army life. Then you get a fresh start with someone that you are not on the radar for and you can be the Soldier that we all want in our team.

For the love of Christ, know that your internet comments are seen by all, and live on long after this storm blows over. There is a fair to middling chance that your Social Media is being monitored, so do not incriminate yourself further by showing your ass to the world in a quest for support/ sympathy. All the internet support in the world and likes on facebook plus a bag of potato chips gets you a bag of potato chips and an Article 15.
Your post above also makes it abundantly clear that you did not learn your lesson and used yet another banned cell phone to post to RP. I would reconsider my priorities, if I were you.

You can listen to me or not. After all, I'm old and just don't understand the hell that is AIT these days. Most comments you will get on this thread will be more blunt, maybe even hostile and unhelpful. I am really trying to help you, if you will take the time to read, heed, and make the adjustment.
Good luck, PVT (Join to see) . I hope you figure out what will be your best path forward.

You should definitely report this to the 1SG, especially tell the 1SG you kept a phone you were required to turn in.
Keep your room squared away, and go back and read up a bit on Army Values and the UCMJ.
Your DS doesn't hate your or anyone else. It's likely your behavior, such as not keeping your room clean, and disobeying a lawful order. This behavior would lead an experienced DS to believe there is other behavior. This behavior goes against good order and discipline.

Man are you the definition of stupid! Do you honestly think the rules in your bay or your training platoon are for someone else and not you? You deserve everything that DI is going to give you. They are not picking on you, they are trying to make you see that you are important as a team member and not an individual. Get rid of all this "me" and "I" crap you keep referring to. Your friends are not your friends if they are telling you to go over your DI's head to the 1st Sgt. Your DI obviously had reason to look in your locker and found the phone you were hiding. Why not spend the additional effort to make that DI proud of you instead of trying to get by all the time? You could be excelling and instead are trying to cheat the system. Grow Up!

Just think prior to social media recruits would call home with their problems. I feel like an old grandpa or a fat uncle answering the phone when I'm reading this. This is the part when your "mom" hands me the phone and says, "can you say something, you were in the army?" Then I'll take the phone and say something like, "hey bud, so you're old job at Walmart is waiting for you if things aren't working out" and hang up.

This was one loooooong sentence followed by one short sentence. I had to read and re-read it three times just to be sure I am understanding the issue.

1) "the first 2 weeks we did get off on the wrong hand but I just wasn’t use to the freedom coming fresh out of basic": You dumped your military bearing and discipline and did something you were supposed to and got in trouble. Making yourself a target
2) "I’ve been staying under the radar for a while but she just looks for any and everything to chow us out about or give us a counseling": Clearly you have not been staying under the radar.
3) "we had a random room expectation and our rooms got trashed": Your room would not have been trashed had your room been squared away in the first place. Also, didn't your barracks in Basic get destroyed after inspections because people did't do what they were supposed to do? Same thing only on a smaller scale. I'm betting dollars to pesos your room got the tornado treatment because it wasn't to standard and was shown to the other Soldiers as an example as to what will happen if the standard is not met.
4) You broke the rules about having an additional phone. How do you forget you had an additional phone? That is in YOUR personal bag?

Sure, go ahead and speak with your 1SG but be sure to tell the WHOLE story to include details about how you kept a dirty room, broke rules, and had an unauthorized phone. You established yourself as a problem child pretty much right off the bat and are now suffering the consequences. Own up and man up. Seriously, quit talking to the Barracks lawyers because you are getting bad intel. Your DS knew you had an additional phone (which is against the rules/policies of the company if I understood your rant properly) and ordered you to open your locker so that she can search and secure it. Nothing illegal that I can tell. But, if you want confirmation, I am certain that there are Company Policy Letters posted stating what can and can't be done in regards to wall locker inspections. If you want to have a better time while in AIT, I suggest you perform/conduct a cranial-rectal extraction procedure, start following the rules to the letter, do what you are supposed to be doing and I guarantee that your DS will ease it up on you and begin to focus on a different problem Soldier. Also, (I'm asking this more out of curiosity) why in the world did you TAG the categories of MAJ, Brig Gen and Cadet 1SG in your post?

Oh young troop...first off, a Drill Sergeant doesn't need your permission to open your wall locker. Your wall locker is an inspectable item. If the Drill Sergeant wants to see what is in your wall locker, he or she has every right to tell you to the pop the lock. It's part of the process of learning the Army way. Then, you had an unauthorized item that you knew was wrong to have. If I was your Drill Sergeant and I knew you had a history of run-ins, I too would show you more love. I'd be in your room daily looking for things and finding something would only ramp me up more. If I were in your shoes, I would bust my fourth point of contact and get myself on course. The fewer reasons you give an NCO to be in your face, the less they will be in your face. I think the Drill Sergeant acted well within her duties and responsibilities.

1. You brought this on yourself by choosing to break the rules.
2. If you quit f*cking up this will eventually blow over. Trust me, someone else will make themselves the new target quickly enough.
3. Stop looking for excuses.
4. If you can't take 8 weeks of being forced to live by simple rules you are never going to make it.
5. The 1SGT will likely throat punch you if you go to him with this BS.

Good time to sit back a re-evaluate life PVT. This is simple, you were tore up, your DS is getting you on the right path. Army values young one, integrity sound familiar? If you are doing the right thing your stuff won't get tossed and your wall locker won't be searched.

I once had my entire room thrown out a second story window because I didn't make sure my battle was squared away, notice how I said "once". Learn from it and move on.

Hell..I was drafted in 1972 and sent to Ft. Polk for basic,..back when they could go hands on with you...we were taught Drills were God and there for 1 reason, to train you to be a fighting unit to make sure you didn't come home in a body bag...all my DS's had at least 1 tour of Nam....quit the whining,..clean the sh** out of your ears and conform to the training....your life might depend on it someday....