Wa'alaikumassalam sis! Those red spots on hands, feet and back sound like they could be early signs of HFMD, especially since the nursery has cases, a few of my mum friends noticed the rash appeared before or without fever in their kids too. Since he's been exposed and showing these symptoms, best to check with the doctor quickly lah, they can confirm properly and advise on what to do next, plus make sure he rests well and drinks plenty of fluids while you wait for the appointment. Fingers crossed it's mild if it is HFMD!