Eva, glad to read that you are going to finish your degree first. Do NOT enlist, as PRS said.
About flying/passing the medical. What PRS said is absolutely true. You may be able to pass an entrance physical, then DQ later after being in training. During flight training, you will take more than one physical. We called them class 1 physicals. They are very thorough. Apparently the first one is what they called a class 1A physical. It was compared to an astronaut candidate's physical. They aren't playing around, it was the most thorough physical I've ever had. While I was at Fort Rucker, we had at least three out 30 candidates fail their physical while in training and subsequently pulled from training.
If you decide to go for it, your attitude will serve you well. Our country and our military needs people just like you.