Swollen eyelid - could it be from an allergy?

Possibly yes. Swelling of the lids is common in allergy because the eyelid skin is very thin and sensitive. Some people can be allergic to cosmetics that only cause eyelid reactions (not other parts of the face or body). With allergy, usually the lids of both eyes are swollen and itching is prominent. Cool compresses and antihistamines can relieve the swelling.