Ft Benning in August is brutal enough with the heat and humidity! And if you need medical attention from the get go, the drill instructors and other trainees will be merciless. You'll get medical attention but you'll also get more than your fair share of verbal abuse.
What type of exercises do you mostly do? Google Neer Test and Hawkins Test. As honestly as possible, perform those tests and see how you feel.
For now, drop ALL straight bar benching, over head pressing (bar or db), and any behind the neck pushing or pulling. Also, if you're one of those guys who still do upright rows, drop that as well.
If you do those tests, and get back to us with your log, we can shed some more light on the subject.