Hello Mary
do use any chemicals, household cleaners, etc? These can be very harsh on skin, even more so if you have sensitive skin. Have you had this skin condition checked out by your GP, you might have an allergy? Whats your bg levels like, some people complain of dry skin, especially if their bg levels are higher than they should be.
If you wear rubber gloves to do the housework, put on a pair of cotton gloves to wear underneath the rubber gloves even if they are lined.
My skin sometimes becomes sore and cracked, I am an outdoors person and the wind and cold can play havoc with my hands if I am not careful. Get hold of Neutrogena Norwegian Forumula handcream (any chemist or supermarket usually sell this product), apply it thickly before you go to bed, then put on cotton gloves or cotton socks over them and leave overnight, see if that makes a difference, repeat as necessary. Use unperfumed products on your skin to avoid irritation. Always dry your hands if they have been in water.
All the best, hope you will feel more comfortable soon