You have not mentioned the site of the lesion.
Is it in the region covered by the cast? or somewhere near the edges of the cast?
If in the region covered by the cast, it might be allergic reaction
to the cast.
If near the edges of the cast, it might be due to irritation of the skin due to movement of the limbs or allergy
Since you say its red and peeled, you may apply simple antibacterial creams like mupirocin
for a week that will act as barrier and heal the infection if any.
If its not getting better/ spreading to other areas, please visit your Pediatrician
as some skin problems too can be seen in association with arthrogryposis
Hope my answer helps you.