No one expects you to be a superhuman, we all have human bodies, we all get sick (Including your instructors).
Show up, they will see your prescription, tell them you're sick, and try your damnedest. You've waited how long for this opportunity right?
Your first while there, it's alot of classroom anyways, you're not running the gauntlet and crawling under barbed wire day one. If you fail the PT test, which you wont be the only one, you get another chance later, it's a long(ish) course. You have alot of time to heal and alot of opportunities to do your best on PT and get in better shape.
To sum up, if you want it badly, try hard, don't quit, your best is all that can be asked of you.
-Cheers!