My skin is peeling off of my fingers and hands, could it be an allergic reaction?

No: Allergic reactions are different, peeling off skin can be due to other reasons, dry skin is one. The peeled skin skin is simply a dead skin being shed out, if you are really suffering see your doctor,

No: This type of reaction is likely from too much exposure to water,soap , or irritant solvent. Suggest that you avoid scented or antibacterial soaps and use hand lotion after washing whenever possible.