Is a swollen eyelid a possible allergic reaction?

Yes, it could be: Swelling (or edema) is a common sign of allergy. It is frequently accompanied by itching and redness. If only one eyelid is affected, it is likely not related to an airborne allergen, but perhaps transfer of an allergen from the hands. Another possibility is an infection of the eyelid area. If pain, fever or vision changes, have it checked out.