Amoxicillin-induced morbilliform rash: This is the most common type of drug rash and is often seen in children after taking amoxicillin. The rash typically appears as diffuse erythematous macules and papules, which can have a white halo, and usually occurs within a week of starting the medication.

Viral exanthem: Many viral infections can cause a rash that appears as erythematous macules with a white halo. Given the age of the child and the timing of the rash, a viral etiology is possible, especially if the child has been exposed to common childhood viruses.
Allergic contact dermatitis: Although less likely given the diffuse nature of the rash, an allergic reaction to another substance (not necessarily amoxicillin) could cause a similar appearance.

Kawasaki disease: Although the rash in Kawasaki disease is typically more polymorphic, it's crucial to consider this diagnosis due to its potential for serious cardiac complications. The presence of fever, conjunctivitis, and changes to the lips and hands would support this diagnosis.
Stevens-Johnson syndrome (SJS) or Toxic Epidermal Necrolysis (TEN): These are severe skin and mucous membrane disorders, usually caused by medications, including antibiotics like amoxicillin. Early recognition is critical due to the high morbidity and mortality associated with these conditions.

Erythema multiforme: Characterized by target lesions, this condition can be triggered by medications, including antibiotics, and viral infections. It's less common in this age group but should be considered if the rash has a distinctive targetoid appearance.
Drug Reaction with Eosinophilia and Systemic Symptoms (DRESS): A rare but potentially life-threatening condition that can occur with certain medications, including antibiotics. It's characterized by a rash, fever, lymphadenopathy, and internal organ involvement.