Periorbital cellulitis: This is a common and likely diagnosis, given the symptoms of swelling and redness under one eye. It is an infection of the skin and tissues around the eye, often caused by bacteria such as Staphylococcus aureus or Streptococcus pyogenes.

Allergic reaction: An allergic reaction to an insect bite, makeup, or other substances can cause swelling and redness under the eye.
Hordeolum (stye): A stye is a localized infection or inflammation of the eyelid margin, which can cause swelling and redness under the eye.
Blepharitis: This is an inflammation of the eyelids, often caused by a bacterial or demodex mite infestation, which can lead to swelling and redness under the eye.

Orbital cellulitis: Although less common than periorbital cellulitis, orbital cellulitis is a serious infection of the tissues surrounding the eye, which can lead to vision loss and other complications if not promptly treated.
Cavernous sinus thrombosis: This is a rare but potentially life-threatening condition that can occur as a complication of facial infections, including those causing swelling and redness under the eye.
Herpes zoster (shingles): If the swelling and redness are accompanied by a rash or blisters, herpes zoster should be considered, as it can lead to serious complications if not treated promptly.

Angioedema: A rare but potentially life-threatening condition characterized by rapid swelling of the skin and mucous membranes, which can cause swelling under the eye.
Granuloma faciale: A rare skin condition that can cause swelling and redness under the eye, often accompanied by a rash or lesions.
Sarcoidosis: A rare autoimmune disease that can cause swelling and redness under the eye, often accompanied by other systemic symptoms.