I found an article by Mary Shomon about the muscle pain of hypoT. I'll have to paraphrase her words, so I hope I have this correct --
Hypothyroidism is known to cause myopathies, the medical term for diseases that affect skeletal muscle. Myopathies most often are seen in the thigh and shoulder area, the large muscles which are closest to the center of the body. In myopathies such as those caused by autoimmune thyroid disease, white blood cells may attack parts of the muscle and the surrounding blood vessels, or abnormal levels of certain biochemical substances end up accumulating in your muscles, leading to weakness or pain.
If time and meds don't make a significant improvement in my shoulder pain, I think I'll explore other avenues... massage or even accupuncture. Perhaps my chiropractor may know something about this. I should ask him. Meanwhile, I keep my Bed Buddy handy. If you don't know what I'm talking about, try a heating pad with moist heat... it should be about the same thing, just not as portable. I can walk around and do my housework with the Bed Buddy on. For some reason, this gizmo works better for me than a hot shower or bath in easing the tension.