An insect stung my eyelid and it has swelled badly. What should I do?

Seek medical help. Your eyes should be taken seriously. It could be a few things including; an allergic reaction, corneal abrasion from rubbing, etc;. See a doctor now and have him/her check it out. They may refer you to an ophthalmologist.
See a doctor. It could be an allergic reaction or an infection or both. See your ophthalmologist.