Will the Army take my blood pressure whenever I go to the dentist? If so, what if it's high? Will I get discharged?

To lower your blood pressure, close your eyes and focus on your breathing. Full breath in and slowly release.

If your blood pressure wasn't high enough to bar you from enlistment a few months ago, it's not going to be high enough to get you kicked out. You're going to get your BP taken a lot in the Army, best to get used to it now

Eating raw garlic helps lol

Not at the Dentist.

I had to get blood pressure monitoring for 24hrs since ive been in and turns out i have pre-hypertension only when im at work lol. you will be fine.

There is such a thing as "white coat syndrome". Basically, a person gets nervous and anxious during a medical examination. It causes your BP, heart rate, and respiration to increase. It's a known phenomena in the medical field. If your BP wasn't high enough to disqualify you from initial enlistment, I don't imagine you'll have any issues during a dental exam. Most dental offices don't routinely take BP (or at least none of mine ever did) unless you're going in for surgery and will be administered general anesthetic.

I'd be more concerned with untreated hypertension (high blood pressure). It can case all sorts of serious issues if not properly managed. Take a few deep breaths, try to relax, and speak with your primary care provider at the earliest opportunity.

I had high blood pressure after my third year in.
I was required to report to the TMC every day @ 1600 to have my B/P taken. If it was high, I was told to go to barracks and rest, if not, all good.
I PCS and expect the same, guess what, no record of of any of this.
I get out and file for C&P to cover cost of B/P meds, no record in my files.
I had to find a couple of my old supervisors (thank god for F/B) and a medic that all wrote statements on my behalf.
I wouldn't sweat it.

You are in AIT. Focus on your MOS and start asking your leadership for answers to all of your questions.