Do you feel stretched out at all on your bike? At 5'1" on a Large if you have a long stem (110/120mm) on there you could be a bit stretched out, but being stretched out shouldn't cause wrist/hand pain. Check the angle on those grips and as said the angle on your controls (brake/shift levers) they should not be so close to parallel that they make you roll you wrist back and not so far down to make you reach for them.
Next check the angle of your saddle, make sure the "sit" part is level to the ground and not tilted forward/down - if mine is titlted down/forward at all it only takes me not even a 1/4 mile before I feel pressure/pain in my hands/wrists. FYI the nose of my sadddle looks up, so that the sit part is level; I use a WTB PureV.
Next check and see how much drop there is between your saddle height and bar height, some people prefer them level, some like a little drop - about 1-2" but that depends on your flexibility. If your stem is flipped down by any chance then turn/flip it the other way so it's a positive rise OR if you have spacers above your stem, remove stem and put them below it. If neither of the two options are available you might need to consider a higher rise stem or bar.
If you can take some pics of the bike side on by itself and with you on it, study them and see if you can notice anything strange and if you want post them up here and maybe we can offer soem more advice. Giving fit advice "blind" on the net is hard, but photos of the person on the bike will usually help alot.