Fever and cough persist, a faint rash comes on: Another viral syndrome?

As the attending on the community hospital's general pediatric service, you're called in this afternoon to see a 9-year-old girl who was admitted the evening before for chief complaints of a fever (axillary temperature, 102° F to 103° F) and cough of five days' duration. She has been observed to have a dry hacking cough, and broke out in a faint rash after admission. Can you solve this Pediatric Puzzler?