Shea butter. Try using a paraben/phthalate-free cream or lotion at night that contains natural oils, like grape seed, jojoba, or olive oil with shea butter. Apply this to your hands at bedtime and wear soft gloves over them through the night. If this doesn't work, you may need to evaluate your fatty acid status and increase supplementation of either omega3 FAS or gla.
Emollients,steroids. Otc emollient such as cerave is a start. However if this is not enough you may have hand eczema which requires prescription strength creams as well as possible patch testing to identify any chemicals which may be causing allergic reaction. Testing is non invasive and requires patches stay on back 48-72 hours.