Orbital Decompression without Graves Disease! (photo)

It does appear that you have congenital bulgy eyes that can benefit from cosmetic orbital decompression. Orbital decompression is not only for patient with thyroid eye disease.  

That would be typical eye changes associated with Grave's disease but without thyroid changes.  Also the eye disease and the thyroid disease do not always go hand in hand.  For orbital decompression, some oculoplastic surgeons do much more orbital decompression work than others.  Robert Goldberg M.D. at UCLA and Michael Kazim, M.D. at Columbia come to mind.

It is important to note that Graves eye disease is not always associated with high or low thyroid levels. Very often the thyroid levels are normal in the beginning (euthyroid Graves disease).  Graves eye disease is the most common reason people develop proptosis (prominent eyes) and should always be first on the list of possible diagnoses.  This can be confirmed by CT imaging looking at the size of the extraocular muscles and where exactly they are enlarged.  An oculoplastic surgeon should evaluate you prior to considering any procedure to correct this. It is imperative that your eyes be stable for 6-12 months before proceeding with decompression. You also should be informed about the side effects, including double vision, asymmetry and changes in eyelid position, which may require further surgery.