extend your arms out in front of you fully, palms facing the floor, hands flat.
with your arms still extended, lift your hands upright like you're telling someone to stop but try to pull your fingers back toward your body. do not force it, just stretch. do this for 15 seconds.
now, arms still outstretched, point your fingers at the ground and try to pull your palms to your body (again, unassisted). hold this for 15 seconds.
now go loose and shake your hands/arms gently.
get a more ergonomic keyboard and mouse. i use a kinesis advantage with no tactile bump on the keys and an evoluent vertical mouse. maybe consider a trackball or some other neutral mouse. split keyboards help.
don't bang the keys so hard, keep your body in a neutral position while you type. don't lean on your keyboard.
maybe get some wrist braces and see a doctor, lain. <3