I teach water aerobics so my nails are in chlorine every day for several hours. At one point I had such a bad split I used super glue to hold it in place until the nail grew out.
Burt's Bees makes a wonderful cuticle cream and hand lotion. Those have helped greatly. Also, Mary Kay sells a cream that I've used as well.
Be sure to get checked out by your doctor, but I can say these lotions have helped.