Finding time to work out isn't as hard as you'd think. All you really need is one hour, three times a week. That includes time to shower and change. Just get up an hour earlier, or stay on campus an hour later... I'm assuming your school has a gym.
For your posture, I'd start by strengthening your lower back. Try
Low Back Extensions or
Deadlifts. The deadlifts'll work your glutes (ass muscles) too.
You'll probably find that a lot of your muscle and joint problems will go away if you start working out, I find it helps me keep my mind alert too, which is another big plus for a student.