This may sound strange, but as an LCSW I have helped a number of clients handle SSI applications. None of mine have ever received it for Graves, but a few have reapplied with the diagnosis of Auto-immune.
Sounds silly to me but they seam to prefer that diagnosis. I would discuss with your providers as they are the ones that will be handling this and are better equipped to provide you with situation specific advise.
Hope this helps
Ann