I would say any RSI activity would cause tennis elbow (even although you don't play probably), I would suggest a visit to your GP for some NSAIDS and for your consideration, perhaps a little ice/heat treatment for a few days to see if it settles down.
If it remains then you might consider a cortisone injection at the site of the pain. However, injections like this don't always work but in saying that the vast majority do if applied correctly. Maybe a little rest for a few days to let the inflammation ease as well as some massage on the extensors to facilitate some healing to begin with.
Hope this helps.
ps. see thread under health & fitness.viewforum.php?f=4