Hordeolum (Stye): This is the most likely diagnosis given the presentation of an eyelid bump. A hordeolum is an acute, localized infection or inflammation of the eyelid margin involving hair follicles of the eyelashes (external hordeolum) or meibomian glands (internal hordeolum).

Chalazion: A chalazion is a small bump on the eyelid due to a blocked oil gland. It is similar to a hordeolum but tends to be larger and less painful. The presentation can be similar, but the lack of acute inflammation and pain might distinguish it from a hordeolum.
Blepharitis: This is an inflammation of the eyelids that can cause redness, itching, and swelling. While it's more of a condition affecting the eyelid margin rather than a distinct "bump," it can sometimes present with or contribute to the formation of eyelid bumps.
Keratosis: A benign growth on the eyelid that can appear as a bump. It's less common than hordeolum or chalazion but should be considered in the differential diagnosis.

Orbital Cellulitis: Although less likely, this is a serious infection of the tissues surrounding the eye, which can present with eyelid swelling and redness. It requires prompt medical attention to prevent serious complications.
Basal Cell Carcinoma or Other Malignancies: While rare, any persistent or growing eyelid bump should be evaluated for the possibility of skin cancer. Early detection is crucial for effective treatment.

Xanthelasma: These are small, yellowish patches or bumps on the eyelids due to accumulation of fat. They are usually harmless but can be a sign of lipid disorders.
Molluscum Contagiosum: A viral infection that can cause small, pearly, or flesh-colored bumps on the skin, including the eyelids. It's contagious and can be spread by direct contact.
Syringoma: Benign tumors of the sweat glands that can appear as small bumps on the eyelids. They are more common in women and can be associated with Down syndrome.