Hello,
Various possibilities for peeling hands are trauma and allergic or irritant contact dermatitis,sometimes cold, dry air can cause peeling and dermatitis or fungal infections can also cause peeling. In your case I feel that it can be due to eczema or contact dermatitis.
Wash the areas several times with fresh water. Do not use any cosmetic products at the sites.You can apply some calamine lotion at the rash as it will help in soothing the skin. For mild-moderate symptoms a weak steroid may be used (e.g. hydrocortisone as dermacort), whilst more severe cases require a higher-potency steroid (e.g. clobetasol propionate, fluocinonide).
Symptoms can be exacerbated by dryness of the skin. Use good quality moisturizers to prevent moisture loss from the skin.
If still the symptoms do not improve then pls get a clinical examination done by a dermatologist. Fungal infections have to be ruled out then.
Hope it helps. Take care and pls do keep me posted on how you are doing or if you have any additional queries.Kind regards.
Cheriopompholyx it is, and would respond to just moisturiser.Severe types need antibiotic internal.