one question i would like to ask you would be if the initials lesion were itchy and if the inter digital areas of hand were also involved, if yes this could be scabies
or some though the lesion on face is qiuet unusual.
also if no other systemic symptoms like fever malaise
, etc were associated, it also points towards scabies or some kind of allergy
its not unusual for lesion of scabies to heal with peeling of skin so you should not worry much if its scabies.
some allergies also may cause these king of papular lesions or bumps that may cause peeling of skin.
so u should not have any reason to worry much if the child is doing fine otherwise and free of any other complaints and wait for few days.
but if you think there is some other new problem or the condition is getting worse you can contact your pediatrician
for advice , and examine physically, he would be in a better position to assess the illness, if it needs any treatment.