Hello and hope you are doing well.
Eczema is one condition where the hands get dry and peeling occurs. In this disorder contact with triggering factors like soaps, cosmetics, jewelry, clothing, and detergents causes symptoms. Sometimes sweat, changes in temperature and psychological stress are known to trigger these episodes. The best way is to prevent attacks by identify those substances which you are allergic to and avoid them. So, Allergy testing would be worth looking into. And treatment is with cortisone based creams, which need to be very potent and of increased strength to heal the cracks. Always wear gloves for washing and while going outside, as cold increases drying. Don't wash your hands anymore than necessary and use very mild soaps. Apply constantly plenty of good moisturizing creams and alternate with steroid creams. Use a humidifier in the rooms to avoid dryness.
You will need to consult your primary care physician for proper assessment, who may then refer you to a dermatologist if needed.
Hope this helped and do keep us posted.
I agree with the top poster. And drink a lot of water. Water is very good for the skin and keeps it hydrated.
try using an emmolient cream if your hand is dry. I find it very helpful. If it's extremely itchy maybe you need some medicated cream.