Allergic Conjunctivitis: This is the most likely diagnosis given the symptoms of eye swelling and redness without fever or pain. Allergic conjunctivitis is common in children and can be triggered by various allergens such as pollen, dust, or pet dander.

Viral Conjunctivitis: Although the absence of fever makes this less likely, viral conjunctivitis can still occur without systemic symptoms. It's highly contagious and can cause significant discomfort.
Blepharitis: This condition involves inflammation of the eyelids and can cause redness and swelling. It's often associated with poor eyelid hygiene or conditions like eczema.
Periorbital Cellulitis: This is an infection of the skin and tissues around the eye, which can cause swelling and redness. The absence of fever and pain makes this less likely, but it cannot be ruled out without further examination.

Orbital Cellulitis: Although less likely due to the absence of fever and pain, orbital cellulitis is a serious infection of the tissues surrounding the eye that can lead to severe complications, including vision loss. It requires prompt antibiotic treatment.
Retinoblastoma: While extremely rare, retinoblastoma is a type of eye cancer that can present with swelling or redness of the eye in children. Early detection is crucial for effective treatment.

Kawasaki Disease: This rare condition can cause eye swelling and redness among other symptoms like fever, rash, and swollen lymph nodes. It's an important diagnosis to consider due to its potential for cardiac complications.
Granulomatosis with Polyangiitis (formerly known as Wegener's Granulomatosis): A rare autoimmune disorder that can affect various parts of the body, including the eyes, causing inflammation and damage.
Erythema Multiforme: A skin condition that can also affect the eyes, causing redness and swelling, often in response to an infection or medication.