It sounds a lot like carpal tunnel to me. Nine times out of ten it will disappear once bubby arrives, I had it for about 3 days after Zander was born then it disappeared as quickly as it had arrived. It's because of fluid build up.

Is it worse in the mornings? Some people wear wrist braces overnight to help or like I did, you can sleep with your arms raised on pillows to help stop the fluid pooling in the carpal tunnel which is what causes the pain.