Mr. bkearns, all of these drummers above have really good suggestions.
Please, see a doctor before it gets any worse. We wouldn't want to loose a drummer. Also ask your doctor to refer you to a pain management doctor and get an MRI done on your hands. An x-ray alone will not show if you that's the only problem.
I would also suggest that you soak your hands in Epsom salts and warm water, and get some Tiger's Balm (An old Chinese balm) found in most local drug stores and wear cotton gloves for a couple of hours so as to make the balm seep in for pain relief.
All persons tend to sleep with their wrists folded inwards. Get some Carpal Sleep Wrist Supports to prevent your wrist from folding overnight. They can be found at your local surgical supply store. This is what they look like: Carpal Sleep Wrist Support
Slingerland Great find on those gloves.
CJDG, great find on the web.
Great advise from all of you drummers.