Final answer:
The most likely diagnosis for the patient, given the symptoms, is Kawasaki disease, which is characterized by prolonged fever, rash, conjunctival congestion, extremity changes, cervical lymphadenopathy, and oral changes.
Step-by-step explanation:
Based on the clinical presentation of high fever, conjunctivitis, diffuse lymphadenopathy, peeling skin around the fingernails, and target-like, erythematous, macular lesions on the trunk and extremities, as well as the absence of tonsillar exudates and purulent drainage of conjunctiva, Kawasaki disease is the most likely diagnosis for this patient. Other conditions such as drug hypersensitivity, scarlet fever, erythema infectiosum (Fifth disease), or Rocky Mountain spotted fever offer partial overlap in symptoms, but do not fully match the unique presentation observed in this case. Kawasaki disease is characterized by prolonged fever, rash, conjunctival congestion, changes in extremities (erythema, edema, or peeling), cervical lymphadenopathy, and oral changes such as strawberry tongue. Kawasaki disease requires prompt treatment to reduce the risk of coronary artery complications.