Is it permissible to use a skin peeling cream to treat hand sensitivity, especially if it contains alcohol, and would that fall under the حديث (Hadith) of cursing?

There is no harm in removing the traces of allergy from the hand with creams, as this is a form of treatment. If it is for removing a defect, there is no harm in it. However, it is forbidden to use creams containing intoxicating alcohol.