Sounds like my youngest daughters hands/nails.

Here's what our doc told her:
1)Drink more water. We tend to drink more in the summer.
2)Shower/bathe/wash hands in warm, not hot water.
3)Use a mild soap. (for ex. Aveeno Cleansing Bar for Dry Skin)
4)Immediately after washing, pat skin dry & apply moisturizer while skin is still damp.
5)Lower temperature and use a humidifier in the house.
6)Use gloves when doing household chores.
7)Apply a generous amount of moisturizer before bed and wear cotton gloves or socks on your hands at night.
8)Use moisturizer with No fragrance and No dyes.

Some moisturizers our doc recommended are:
Eucerin
Aveeno
Nivca
Vaseline Creamy

Good luck!