It is very definitely bursitis. I had investigational ultrasound, as I do with all soft-tissue problems, as it is the ONLY way to factually verify what the problem is, and the ONLY way to ensure that an injection goes into the right place. I have had useless injections from doctors who did not use it and assumed they knew where to put it. The inflammation can be in a different place from the pain. So, I had injections, which helped a little, but not enough, not permanently.
I have to carry grocery bags a couple of times a week, and I seem to be able to tolerate that dead hang, and I flex my arms slightly. If I flex them more than 25 percent or so, the biceps tendons will inflame. I used to swim, but that was prolonging the problem.
I have had physical therapy, and that is rarely helpful. I found some information online that may work better if I apply it. If I could afford a sophisticated trainer or something, it would help, perhaps. I think having gentle massage immediately after exercise could relieve it better. Serious massages do not help at all!