Trying to rough it for the sake of grades is not a good idea. I've tried it before and it's awful. My sickness would make it so that I couldn't focus well, and I would have to spend alot of class time constantly getting up to blow my nose, or go to the bathroom and use toilet paper if the teacher didn't have tissues. Headaches would be awful too, and the worst feeling for me would be entering cold rooms. It's not worth it. Stay at home.
It also sounds like your immune system is not very strong. Not sure if that's hereditary for you or just because you don't get enough exercise or take supplements.