I get my thyroid tested every three months on my own dime since taking over my own health and not relying on someone in a white coat. I get TSH, free T3, free T4, TPO and Thyroglobulin Antibodies. I get this done by way of the Internet through my med lab dot com for $175 a pop, and no doctor visit or office copay involved. You do have to visit a lab for a blood draw, but that's it. Best of all, you can chart your results on their website which makes monitoring your progress a breeze. The test I get is called the Thyroid Complete Panel, but there are others as well. Just go to the link below, click on TESTS and type thyroid in the search bar and a whole menu pops up.
They have every type of blood test you can imagine and more. If you want to take control of your health, this is a good first step in that direction. I started doing this when my primary care physician as well as my endocrinologist would not test my blood for thyroid antibodies, telling me there was no point in it since there was nothing I could do that would affect them. That turned out to be untrue.