What happens if a mosquito bites your eye?

Itching and swelling. A mosquito bite around the eye may cause sifnificant swelling, itching & discomfort depending on your particular reaction to bites. The eye is prone to swell due to the laxity of the surrounding tissue. Use cold compresses, perhaps appropriately take an antihistamine like "benadryl" & avoid scratching. Expect the eye to close in a severe case. If concerned, see pcp. Often more bark than bite!
Swelling. Watch out for redness in the area especially if you have been scratching around the area. You can develop an infection called "cellulitis" of the skin which may need treatment.