These kind of hands can be due to eczema, contact dermatitis and contact with harsh detergents, soaps and lotions. Sometimes cold, dry air can cause peeling and dermatitis or fungal infections can also cause peeling.
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, whilst more severe cases require a higher-potency steroid.
Symptoms can be exacerbated by dryness of the skin. Use good quality moisturizers to prevent moisture loss from the skin. During the day, hydrate and protect hands with a protective and moisturizing cream. At night, repair them with creams formulated from glycolic acid—a must for improving skin texture and tone. If still the symptoms do not improve then please get a clinical examination done by a dermatologist. Fungal infections and eczema have to be ruled out then.
I hope it helps. It is very difficult to precisely confirm a diagnosis without examination and investigations and the answer is based on the medical information provided. For exact diagnosis, you are requested to consult your doctor. I sincerely hope that helps. Take care and please do keep me posted on how you are doing.
Do you have any pictures of your hands?
It would really help me get an idea of what your talking about.
(Martikadragoon CL Dermatology)