Well, I don't want to discourage any left handed bowler from converting to the 'real bowlers' side, but your arm health is the more important thing.
Don't get discouraged about the tendonitis. Regardless of what you've been told, with the right therapy and a little bit of rest, you can beat it. Check out the following therapies:
http://www.astym.com/http://www.activerelease.com/I tried everything before using the above two techniques. I went from barely being able to lift a ball in November 2008 to being a functional hack again by March 2009.
Focus on the soft tissue therapies. I first tried a few months of traditional physical therapy, chiropractic, and acupuncture with little (if any) improvement. I did more research and found out about ASTYM and ART. Three months of intensive therapy, and I'm 90% there.
Soft tissue therapies work.