I am being told to go to PT by the command on only 4-5 hours of sleep. As a junior enlisted, how do I solve this problem?

You sound like all these snowflakes and millennials maybe you should go sell AVON and quit your whining your in the military not in Dora the explorer

I have done PT hungover with no sleep.
Had to dig deep and get it done.
There is no rule that's says you can't lay back down since you don't report to duty til 1600.

Sometime in the near future, my fellow medic, you may end up in a field hospital where you NEVER know when a patient load will suddenly surge and you may have to extend your "shift" and work through 12 - 18 hour DUTY times. Will you have the stamina to carry through or will you request that the casualties stop bleeding long enough for you to take a nap? I flew aeromedical evacuation missions that would go from 17 - 20 hours with little to no time for sleep. While in the Army as a 91C my team would constantly be alerted to return for incoming injuries and your "shift" wasn't over until all had been cared for and bedded down. Even while on the job in the civilian ER I worked it wasn't unusual for a sudden surge in trauma victims that would result in 12 - 16 hour shifts and we had to be back in a few hours for our next assigned shift. Suck it up and get tough, you might just surprise yourself on what you can accomplish. You have the honor of being in a great MOS, do it with pride & honor.

Easy solution: shut up and show up. Jesus guy you’re in the military. You don’t get to just pick and choose which parts you want. At least you have a steady schedule and an easy job. You could be stuck in the field for a couple months with MRE shits and 2 hours of sleep per night.

Go to PT... It will build up your system to help you when you have no sleep at all and still have function.

Hospital staff service members enjoy the comforts of a 9-5 type position. Sounds like the 1SG found out that all or most of his Soldiers are a little to comfy there and are not showing up for PT formation. One of the required formations for a typical unit. The only problem here seems to be a misunderstanding that an order to be at PT formation is an issue or problem as the question is posed. There is no problem. Do your job as a Soldier. That includes being at PT formation.

Something I noticed in your question - you stated "my section is the only one in the hospital that has a 1600-0000 shift." So are there others in your company making it to PT? Just saying if you can demonstrate its not an individual issue might be able to work out an alternate schedule with your top for your section. This may require some creativity to fix but you can do it. However in the mean time show up to PT. Don't piss off you top as it will not help in finding a way to resolve your sleep deprivation.

Sleeps a crutch you don’t need it. Get Deployed, have kids or get a job working midnights in the civilian world.

My initial response is that this isn't problem and to yell at you. But you're young and it DOES suck. Get used to suck. I lat moved after my first enlistment and had midnight shift classes but still had to be up for CO PT. It is what it is. If it helps (at your young age and rank maybe it won't) understand that your CO has a duty to report the fitness level of his company to HIS CO. So, in essence, he has to do this. You made the choice to serve, but I believe (and hope) that you will see that your brothers will serve you right back. Hang in there, toughen up, and you'll be proud of yourself for doing so. Oohrah, soldier!

PT is optional???? Imagine a First Sgt noticing only 5 soldiers at PT! Too late, you do sound like you are whining.