Viral Conjunctivitis: This is the most likely diagnosis given the symptoms of red, itchy, watery eyes that started in one eye and spread to the other, accompanied by a sore throat and mild nasal congestion. The presence of a gritty sensation and the temporary relief provided by artificial tears also support this diagnosis. The recent exposure to her niece who had a "cold" further suggests a viral etiology.

Allergic Conjunctivitis: The itchy eyes and the aggravation of symptoms by exposure to bright light and prolonged screen time could suggest an allergic component. However, the absence of other typical allergic symptoms such as sneezing or coughing makes this less likely than viral conjunctivitis.
Pharyngitis: The sore throat could be indicative of pharyngitis, possibly of viral origin given the context of the patient's other symptoms and recent exposure to someone with a "cold."
Dry Eye Syndrome: The symptoms of dryness, grittiness, and the relief provided by artificial tears could suggest dry eye syndrome, but this would not fully explain the sore throat or the recent onset of symptoms.

Epiglottitis: Although less likely given the absence of severe symptoms such as difficulty swallowing or shortness of breath, epiglottitis is a potentially life-threatening condition that requires prompt recognition and treatment. The presence of a sore throat, even if moderate, warrants consideration of this diagnosis.
Gonococcal Conjunctivitis: This is an important consideration in sexually active individuals, as it can present with similar symptoms of conjunctivitis and can have serious consequences if not treated promptly.
Herpes Simplex Keratitis: This condition can cause eye pain, redness, and discharge, and can lead to serious complications if not recognized and treated appropriately.

Sjögren's Syndrome: An autoimmune disorder that can cause dry eyes and dry mouth, among other symptoms. While it's a less likely explanation for J.K.'s acute presentation, it could be considered if symptoms persist or if there are other systemic symptoms.
Kawasaki Disease: A rare condition that can cause conjunctivitis, among other symptoms, but is typically seen in children and would be unusual in a 28-year-old without other characteristic symptoms such as rash, fever, or lymphadenopathy.