M.P.
It could be eczema caused by irritation such as rings or detergent. I doubt that it's systemic eczema. That would cover more parts of your skin. Cortisone cream should help it to heal. And try to find out what the irritant is.
Or it could be chapped skin. Have you been out in the cold with your hands wet? Emollient cream would help if this is the cause.