If you go to an off post hospital, can anyone in your chain in command request those medical records?

Tricare won't cover your hospital visit unless it's to an ER and it's an emergency and you're away from your Military Treatment Facility.

If you want to go to a doctor on your own dime, then go for it. Your chain of command doesn't have access to your medical records to begin with, but if your peace of mind costs tens of thousands of dollars, then that's the price of a good night's sleep. I've personally never met a SPC with thousands of dollars of spending cash laying around to pay for uninsured medical expenses, but there's always a first for everyone in the Army

If you don't have a referral or it's not an ER visit you're paying out of pocket.

Why do you think your command can access your medical records?

While Tricare does cover ER visits you honestly are doing yourself a disservice by not going to your On-post hospital if you have one. You are covered by HIPPA no matter what. However hiding medical/mental treatment; especially emergencies, from your unit, probably isn't the best idea. I don't know your personal situation but telling your direct-line supervisor will allow you to be sure the military will be tracking your medical health history. And trust me you'll want everything documented for when you get out or especially if and when you need additional treatment.

Additionally, and probably most important, IF your unit DOES find out you went to the off-post ER and you did not tell your direct-line, you'll be in way more trouble than if you just tell them.