Kay, it seems to me your “bright eye” problem is the direct hyperthyroid symptom of lid-lag (elevation of the upper eyelid). According to the many sources, this is the non-infiltrative variety of Thyroid Associated Eye Diesease and will generally reverse symptomically once your Thyroid hormone level is brought down to normal (regardless of what method of treatment is used in controlling the hyper state).
This is the case for most people I know who have Graves (I guess they are lucky). Maybe this is the majority case for Graves suffers…I am not really sure ??
If on the other hand, your eyeballs are really “coming out”, then I suggest you better consult an Opthamologist.
Bye