A 9-year-old girl presents to an outpatient clinic with her guardian complaining of a diffuse rash that started two days ago. Her guardian reports she developed a sore throat, headache, and low-grade fever about five days prior, which initially responded to symptomatic relief measures. However, the fever subsequently worsened to 38.8°C, and a widespread, erythematous rash emerged, prompting this visit. The guardian mentions giving a single dose of amoxicillin, prescribed for a sibling, two days prior, which did not improve symptoms. On examination, her temperature is 38.8°C, pulse is 105/min, respirations are 22/min, and blood pressure is 98/62 mmHg. Her oxygen saturation is 98% on room air. Physical examination reveals tonsillar erythema with some patchy exudates, tender anterior cervical lymphadenopathy, and a prominent erythematous rash with a coarse, papular texture, described as feeling like sandpaper, particularly accentuated in the flexural creases. Her tongue appears red and edematous with prominent papillae, consistent with a 'strawberry tongue'. Based on these clinical findings and initial laboratory results, what is the most likely diagnosis and the appropriate initial management?