Periorbital cellulitis: This condition is an infection of the skin and tissues surrounding the eye, which can cause swelling. The asymmetrical presentation could be due to the initial site of infection or the patient's response to the infection.

Allergic reactions: Allergies can cause swelling around the eyes, and if the allergen exposure was asymmetrical (e.g., an insect bite near one eye), this could result in uneven swelling.
Trauma: Mild injuries to the face can cause swelling that might appear more pronounced above one eye and below the other, depending on the nature and location of the trauma.
Blepharitis: This is an inflammation of the eyelids that can cause swelling, redness, and itching. It might present asymmetrically.

Orbital abscess: Although less common, an abscess behind the eye can cause significant swelling and protrusion of the eye (proptosis). It's a medical emergency requiring prompt treatment.
Cavernous sinus thrombosis: A rare but potentially life-threatening condition that can cause swelling around the eyes, among other symptoms. It's associated with infections in the facial area.
Basal cell carcinoma or other tumors: Though rare, tumors around the eye can cause localized swelling. Early detection is crucial for effective treatment.

Wegener's granulomatosis (Granulomatosis with Polyangiitis): A rare autoimmune disorder that can cause a variety of symptoms, including swelling around the eyes due to inflammation of the blood vessels.
Sarcoidosis: Another autoimmune condition that can lead to swelling and inflammation in various parts of the body, including around the eyes.
Dermatomyositis: An inflammatory disease that can cause skin rash and swelling, including around the eyes, though it's more commonly associated with a heliotrope rash (purple rash around the eyes).