The pads of a few of my child's fingers are red and sore, but almost overnight several fingers (on the pads and sides) started peeling. ?

See a doctor: you need to take your child to the pediatrician .please that is not normal. regardless if allergy or infection, need to be taking care of.

Peeling fingers? : Is there an associated sore throat or fever? Rash in any other location? Does it itch? Any contacts with illness? The child should have an exam to evaluate this. Strep illness can cause a rash that peels in the late stages. Best of luck!

Peeling fingers: Peeling of fingers can be due to many conditions, including kawasaki disease, scarlet fever, skin allergies, skin peeling alone without any other information, is not enough to make any diagnosis, it is very important to take your child to your pediatrician ASAP for physical exam & evaluation. Good luck

See MD: Red rash on hands and peeling fingers can be a serious allergic reaction I recommend you see if physician within the next 12 hours or a dermatologist or go to the emergency department or urgent care

Possible minor burn.: All of these answers are correct. Have you also considered that your child may have touched a hot object--even bricks when outside--and this is a minor burn ?