How do I know if my baby has reyes syndrome?

He'd be dead or ICU. Reye's syndrome was mostly seen in the 1980's, with children having sudden liver failure. It was associated with the use of Aspirin during certain viral infections (flu and chickenpox). Most of these kids died, and all were very, very ill. If your child isn't critically, it is not reye's syndrome. For reasons we don't fully understand, reye's syndrome seems to have largely disappeared.
If you never... ...Gave your child aspirin, the chances are slim to none of ever developing reye's. And reye's syndrome presents with such awful vomiting and coma, any child who looks reasonably ok is highly unlikely to have it.