It depends on what you are describing which we can not really comment on without seeing.
Kindly see a doctor for proper examination and management if their is any issues.

It's nothing to worry about especially if their are no other symptoms. Children often have old skin removed to be replaced by new ones and this may be the cause of the peeling especially if the skin is also dry.
Ensure you keep palms and feet moisturized. If it doesn't get any better please see a dermatologist.

Check the temperature with a digital thermometer first to really know if it is high. Temperature of 36.5 to 37.5 is normal. Anything higher than that give
paracetamol and see a doctor.