Thanks very much for your answers. It is helpful to my understanding of this disease I am new to.
Sorry, I misread that TSI test for TSH. Please do keep in mind the suggested tests, since sooner or later you will most likely need to expand testing to help you get to a euthyroid state, instead of hyper or hypo.
A TSH test is not that expensive, and also not that useful. TSH is a pituitary hormone that is affected by so many variables that at best it is only an indicator, to be considered along with more important indicators such as symptoms, and also levels of the biologically active thyroid hormones, Free T3 and Free T4 (not the same as Total T3 and T4).
How long was it that your doctor wanted you to wait before re-testing? That is probably adequate, unless you find that you are suffering from either continued hyper symptoms, or that your med dosage is too high and you start to notice hypo symptoms. In either case you should then go ahead and call the doctor and relate the symptoms and request to be tested earlier.
I would like to suggest that for now as well as future testing, you should insist on being tested for Free T3 and Free T4, along with TSH, each time you go in for tests. Free T3 is the most important since it largely regulates metabolism and many other body functions. Scientific studies have also shown that Free T3 correlated best with hypo symptoms, while Free T4 and TSH did not correlate at all.
It will be very important to know Free T3 and Free T4 as you continue treatment.
You might want to think about getting tested for Hashimoto's, as well, since some people do have both Graves and Hashimoto's. Those tests are TPOab and TGab.