I am sorry to hear about your problem with a bulging eye. As @JustinMcClanahan, asked I'm wondering what other symptoms you might have related to the eyes. You do not mention your age or whether you have had other eye problems in the past (like surgeries or injuries, etc.).
Have you had a consult by an endocrinologist or just an eye doctor? An endocrinologist might best be able to rule out Graves' Disease as they are experts in the endocrine system that deals with thyroid problems.
You might consider asking for a referral to an endocrinologist.