Since "tennis elbow" and the opposite "golfer's elbow" are both overuse injuries, I would pipe in here and say that listening to your body is wise and allow for some rest. It is really hard to do when you don't want to miss a weekend of paddling, too!
Ice is your friend! As an LMT, it is beyond my scope of practice to recommend anti-inflammatories, but listen to what your friends, MD's and others may recommend. Ice in itself is an anti-inflammatory. Stretching is good and there are strenghtening exercises that can help. Also find a massage therapist in your area who understands working with injuries. Massage can make a world of difference with tennis elbow. I have also found that Kinesio Tape can help too.
Attached is a link to an article I give to my clients on Tennis Elbow. It was originally written for MT's so skip over the massage part, but there are a couple of good stretches and easy exercises with pictures that I give it out for that reason...
http://benbenjamin.com/pdfs/06JJ.pdf
If the problem really persists -see a Dr and get a referral for PT.
Good luck and I hope you heal quickly!!!