Back from the doctor. The doctor I saw went and got another doctor to see me. The way the other doctor was explaining things to the original doctor I was supposed to see, the original didn't know much about the issues with my arm. It could "possibly" be a torn tendon, but don't know yet. They sent me for x-rays and blood work, and prescribed an anti-inflammatory medicine (which my pharmacy said won't be ready until tomorrow afternoon).
I have a return appointment in two weeks, and an appointment with physical therapy on July 9th. If the therapy doesn't work, they will schedule an MRI on the arm. They said I might end up having to see an orthopedic surgeon if nothing else works to stop the pains.