What classes are you taking? I usually suggest a lighter load for the first semester because going away from home for the first time is such a big adjustment to make. As far as your course work is concerned, just be sure to manage your time well, and you might want to consider studying in the library rather than your dorm room (I assume you are in the dorm). It is often more quiet than the dorms. Don't procrastinate, no matter how tempting.

About your homesickness: I am guessing it is somewhat amplified because you are not feeling well and also because your family away on vacation. I bet you will feel less distressed when they come home (and are back to their ordinary lives) and you are feeling better physically.

Hang in there, things will get better. It just takes some time getting through all the "firsts" without your family there. (First time they have a vacation without me, first minor holiday not being at home, first time mom isn't making me soup when I am sick, etc.) You'll be fine; lots of kids go through this.