Sounds similar to the first stages of chicken pox, before the actual lymph filled blisters appear. I had it as an adult. Chest rash, mild fever and lassitude. I consulted a supposed doctor who said I might have fleas in my bedding and suggested bug spray. I still think about that medical quack from time to time.
I thought about that or measles, but he has had his vaccinations and I would hope that the doctors at the children’s hospital would have recognized any of those diseases. Guess you can’t count on that.
Doesn’t sound like chicken pox. I’m an expert. I’ve had it four times. It gets milder each time. I’ve had all the childhood diseases as an adult. Mumps were the worst. This child’s illness sounds like scarlet fever.