What you are dealing with is probably eczema
, which is a condition in which the skin becomes red, itchy, and cracks due to excessive dryness. Sometimes the condition can be provoked by various chemical or other exposures, such as some material in your gloves. However, more likely, you are worsening things by excessive hand washing.
People with eczema should back off on the amount of washing they do. In particular you should limit use of soap and hot water. After each time you wash your hands, you should pat them dry (don't rub them with the towel) and then immediately apply a skin moisturizer for protection.
The type of moisturizer you use is also important. Most lotions and creams are of no use because they are too light to provide adequate protection. It is best to use a 'greasy' product like hydrolated petrolatum, as these are most effective.
You should also talk to your primary care doctor
. This is because many cases of eczema and dry skin need, in addition to skin care and moisturizing, a steroid cream applied to the most stubborn areas of redness and cracking in order to get under good control. Your doctor will be able to help you with this.