Whether your pain is caused by the Graves, or not, there might be some very mild exercises that you can do to alleviate it. I had the frozen shoulder stuff last winter, and did two months of physical terrorpy. (You know that old Samsonite commercial? The one where the gorilla is throwing the suitcases around the baggage area at an airport? Well, there were days when I felt just like the suitcase!) ANYWAY, the exercises that help me the most, and I still do them, CAN do them, even with the Graves, are mild stretching exercises. The way it was explained to me was that the pain can cause the muscles to tighten in response (obviously) and if they respond this way for too long, they tend to shorten, which, in turn, tends to aggravate the pain, especially if it is coming from a nerve. I absolutely swear by the simple exercise that I was given for my shoulder pain. It is very, very gradually, unfreezing, and the pain is now minimal.
I really recommend you get a physical terrorist/doctor/trainer to show you some of these exercises. But, remember, they are STRETCHING exercises, not strengthening ones: the terrorists tend to prefer the latter.
Or, you could email me and I could “try” to describe them. I doubt that would work as well, though.