I have been having the same kind of pain on and off - only in my right arm. I consulted my best friend, who is a basketball coach and knows a lot of sports medicine info, and she said to use heat, stretch and massage, then ice.
And, I have to say, it's working! it helps heal the muscles and tendons. Though, I don't think that it is a long-term solution. I'm glad you started this thread.
2011 Specialized Dolce Elite/stock Riva
2010 Jamis Durango 1 Femme
2006 Diamondback Wildwood (gift from my mother-in-law, so I must keep it! It is really comfy to ride)
1996 Raleigh M-20 (got my love for cycling going!)