I'm confident
@USArmyHPSP provided you an excellent response with all the details. I'm just going to mention a little here for future folks looking for info.
Once your obligation is finished, you're done. You sign a contract with the government that is legally binding and you must abide by the conditions set forth in it.
Once your contract is nearing completion, you are not required to renew. As long as you have fulfilled your obligation to the military, they will not force you to stay.
Yes, STOP LOSS is a thing. But there are lots of rules surrounding it and is very unlikely. But I also can not predict what things will look like ~20 years in the future.
If you're talking about doing orthopedics, you're looking at parting ways from Active Duty around 2032. I'm too lazy to look it up right now, but is it ~6 years? Assuming you match into an ortho program straight out of school (from my understanding is unlikely; for anyone, not you specifically). Again, that is the absolute fastest. It is more likely around 2035ish.
If you are Class of 2020, I believe you are no longer eligible. If there are any 3 year slots remaining, I would guess that packages have been submitted and the spots are filling up fast, if not gone already.
I hope this helped a little. But in case my info conflicts with
@USArmyHPSP I would listen to his guidance as he is the subject matter expert.