Nails are known to crack when they are overexposed to water and home detergents. If you do all the washing of clothes and vessels for your house, you might want to get a helping hand with that. If you cannot get any help right now at least consider getting a milder detergent to save your nails. If this doesn't seem to help, there are, currently, available in the market, certain brands of Instant Liquid Nail Hardeners. How these work is simple - they form a protective coat over the cracked nail and prevent them from developing deeper cracks.
Now about your skin problem - here are some things to do to prevent and even reverse skin peeling. Do not pick at the skin that's peeling. Agreed it might look bad, but any further peeling might hurt further skin and even expose you to infections. Get yourself a good moisturizer and apply all over affected areas. This for sure will greatly help. Also, a gently bath without excessive scrubbing is a great way to soak and heal the dryness. Drink at least 10 glasses of of water a day. This will benefit not only your skin but your general health as well. All the best!
answered by G R