Skin problems are difficult to determine, so you should see a dermatologist (a doctor specializing in skin problems). There can be a variety of causes, but if I had to make a guess, you might have gotten a fungus into the skin of your palms. It would be similar to athletes' foot or jock itch, but in a different area of your body.
Another possibility, if you have tendency to sweat a lot, is clogged sweat ducts. Using talcum powder or cornstarch to absorb the excess sweat sometimes helps.
But as I said before, the best thing would be to see a doctor who can make a determination as to the cause and then direct you to the best cure.

