Thanks Stan and Mighty Buffalo. After bowling last night and paying attention to what my arm was doing, I think you are both correct.
I found that I didn't have pain as long as I focused on keeping the weight of the ball resting on my index during my back-swing, release, and follow-through.
This told me that I had gone back to a bad habit that I thought I had broken years ago. Although, I have an inside-to-out release at the point of delivery, my natural tendency is for my hand to move to the outside of the ball during the back-swing and then manage to return to the inside of the ball by the point of release. It's this exact motion of trying to bring the ball back into position that is causing the pain.
A few years ago I had a lesson at Nationals in Reno and he said that my style is unusual in that, typically, when bowlers' hands move to the outside of the ball during the backswing, they usually keep it outside of the ball through release (like an old-timey full-roller 1960's release). Whereas, I was naturally going to the outside during back-swing and quickly forcing my hand back to the inside before releasing the ball. Obviously, there is a lot of wasted motion in this and apparently it must put too much additional stress on my wrist because the difference was night-and-day when I focused on staying behind the ball by keeping the weight on my index finger throughout the swing last night.
Looks like I'll need to continue working on this and thanks again for pointing me in the right direction.