Natural doctors and natural supplements are not covered by health insurance, but if they order bloodwork, that is covered. I see a RN who is also certified in nutrition and natural medicine. Natural medicine can be very helpful. I believe natural doctors are difficult to find. I found my place by talking to other people in my area. Healthfood stores can be helpful if the person helping you is knowledgable about your condition, but I came across a women at a healthfood store the other day who did not know anything about hyperthyroid. Try searching the internet to see if there is a natural medicine practice in your area.
No typically they are not covered under insurance. Go to your local healthfood store and ask who they recommend or if there is even a holistic doc in your area. In my area we have a holistic type of magazine that comes out monthly that you can find at the healthfood stores, some chiro offices, etc.
I think I wrote back to you on another thread that you could also get a good thyroid support from the healthfood store and start there. Just ask them for a good brand. That would save you a lot of money to start with, or possibly help you feel better until you can find a holistic doc. Good luck!