You may want to also consider asking you primary physician for a referral to an orthopedic surgeon to further investigate the cause of the pain. It could be something as simple as tendonitis, but then it could also be a rotator cuff injury or arthritis.

I've injured my rotator cuff before, (luckily not in my draw arm) it took a long time to heal (probably because I didn't really give it a chance to heal) and tends to get sore again fairly easily. Definitely see your doctor to get the proper referrals.