I puked 4 times in UPT, all related to self-induced stress. Relax & take it in stride, you'll be fine. I taught UPT for 3 years in the T-37, and have only met one person with a genuine medical condition that prevented him from flying: no kidding, 5 minutes into every flight he vomited...he did his best, and concluded a ground job in the USAF was for him.
Don't sweat it...with your current experience you're well over the hump.