Is the pain/lack of strength only present on the bike? If not, maybe see your doctor and get a referral to a WARNING: This post is considered spam by MbPost. All links on this post are considered dangerous..
If it is restricted to the bike, you might be able to troubleshoot it yourself, especially given your experience on the bike.
A few things I thought of:.
Have you changed anything on your bike or with regard to your kit, recently (shoes, pedals, stem etc.)? From my experience very small changes to how things are set up can have a tremendous affect on my comfort?
Have you sustained any (major or minor) other injury before/since you noticed the problem with your hand? A physical problem or imbalance remote from the source of pain could be the culprit. A year and a half ago I injured my left knee while running and the injury brought to the fore the fact that while on the bike I favored my right leg (slight leg length discrepancy). The injury exacerbated the stress on my left leg to the point it was painful to ride more than 1/2 an hour. I've had great success by using shims b/w the cleat and sole of my right (short) leg and also by religiously stretching (so that the underlying problem isn't made more so by general tightness).
As an aside, cycling forums seem to emphasize leg/core stretches; you might look to climbing forums for shoulder/upper arm/lower arm/hand stretches.
If you don't have access to a good sports physical therapist you could also shoot the guys at cyclingnews.com (
fitness@cyclingnews.com) an email and see what they have to say. They have a panel of 'experts' who answer questions such as yours and are much more qualified than whatever anecdotal info I can give. You might even find an answer in their archives.
Best of luck and in the meantime keep riding but ice your hand afterwards!
Aaron