I also have Graves, and just a heads up, I had RAI and not sure what is to blame, the thyroid or the treatment, but I am anemic
and have very low Vitamin d levels, all of which cause
muscle soreness. I took a heavy dose of D and iron and the soreness is going away, although my levels are finally getting back to normal also. This has been since october, that is when I had the RAI.
Have your vitamin levels and iron checked, hope this helps.