How can I improve stamina?

[Quicksilvre]

Nineteen-year-old male here, about 5'10" and 150 lbs, and I have an issue. Well, I have a lot of issues with my health, really, but one issue that I specifically want to address here.

I'm a student, studying at a demanding university taking a demanding major (math) with a chronic illness to boot. My class load is not too bad; I go to 16 hours of class (third year math and physics) and I expect to do about 20-25 hours a homework a week. I'm sure most of you do more at your school/job than I do.

My problem is that I simply have no energy left after that. By the time I make it back to my room all I want to do is either watch TV or take a nap. I've tried going to bed earlier, but all I do is just lie there for a while or get up two hours before my alarm clock goes off. It's very hard to get up and go to the library or pick up a pencil and start working, much less socialize.

I do not get very much exercise. Mostly it's just walking to class or the dining halls, which totals about a mile and a half per day on average. Last year I would walk from campus to downtown, which was a more robust workout--almost two miles round-trip, with a twelve-story climb down and up the stairs leading to town. I think I had somewhat better energy then, but I did have better health as well. My diet is low residue (as little fiber/fried food as possible), but other than that, it's whatever the dining halls have. I average around 200 mg of caffeine a day. There is a full-fledged gym and swimming pool on campus, available to all students.

Is there anything in particular that I ought to be taking in, exercise- or diet-wise? I suspect this means more than just squats and deadlifts (right?).