Blepharitis: This is an inflammation of the eyelids that can cause swelling, pain, and discharge. It's a common condition and can be caused by a bacterial or demodex mite infestation, making it a likely diagnosis given the symptoms.

Conjunctivitis (Pink Eye): This condition, often caused by a viral or bacterial infection, can lead to eyelid swelling, pain, and discharge. It's highly contagious and common, especially in children.
Hordeolum (Stye): A localized infection or inflammation of the eyelid margin involving hair follicles of the eyelashes or meibomian glands. It presents as a painful, swollen nodule on the eyelid, which may discharge.
Chalazion: A small bump on the eyelid due to a blocked oil gland. While often painless, if it becomes infected, it can cause pain, swelling, and discharge.

Orbital Cellulitis: A serious infection of the tissues surrounding the eye, which can cause eyelid swelling, pain, and discharge. It's a medical emergency due to the risk of vision loss and intracranial complications.
Dacryocystitis: An infection of the lacrimal sac, usually caused by a blockage of the nasolacrimal duct. It can present with eyelid swelling, pain, and discharge, particularly if the infection spreads to the surrounding tissues.

Angioedema: A rare condition characterized by the rapid swelling of the dermis, subcutaneous tissue, mucosa, and submucosal tissues. It can cause eyelid swelling but is less commonly associated with discharge.
Eyelid Malignancies: Though rare, certain types of skin cancers (like basal cell carcinoma or squamous cell carcinoma) can present with swelling, pain, and discharge if they become infected or ulcerate.
Trachoma: A chronic infection of the eye caused by Chlamydia trachomatis, leading to eyelid swelling, pain, and discharge, particularly in endemic areas. It's rare in developed countries but significant in areas with poor sanitation and hygiene.