You could your eye doctor to call your family doctor and explain that they suspect Graves and that it's important to have the following tests done: TSI (Graves antibodies), FT3 and FT4. Also, you could ask for a referral to see an endocrinologist.
Yes, that would be the best for now. If the doctor resists, then you should insist on all 3 tests and don't take no for an answer. I would even make sure the lab person drawing blood is aware it is to be Free T3 and Free T4, not Total T3 and Total T4. You'd be surprised how often they operate on auto pilot and do the same old tests as usual, rather than what you wanted.
Thank you for your response. How do you find the right doctor that will order the right tests? My family doctor is who ordered these tests after the eye doctor sent him a letter. Should I ask him to order more?
The definitive test for Graves is the TSI test. Also, you should always test for Free T3 and Free T4 (not the same as Total T3 and Total T4), each time you go in for tests.