Well I am specializing in it.. as a patient.
I would have to go through medical school to become a thyroid specialist. I would if I could build a time machine and tell myself to go to med school versus graduate school. I will do what I can here and for my family and friends.
There are thyroid specialist. Most are associated with universities and have made thyroids their pet projects. However technically an endocrinologist should be able to handle thyroid issues. But you have to take into account how many thyroid issues they encounter and treat. Not enough.. more than 1 in 10 have Hashimoto's antibodies and over 50% are destined to activate (1.3 in 20) and eventually spiral into Hashimoto's hypothyroidism. Now think of how many people you know... if your circle is wide enough.. you should have Hashimoto's sisters/brothers right there with you.. but do they know it? Or are there issues blamed on other things? Right now diabetes is the dominant endocrine focus, it kills much quicker than low thyroid function. Sooo if you had diabetes you would be a shoe in for quick treatment. Now we have to diagnose ourselves for the most part and sweet talk, harass, cry, beg, and whine to get them to do the tests that will confirm or deny our conditions.
Is there a practicing medical hospital near you? Maybe you can get in there? Look on line and research their faculty. You maybe able to enter into a medical study and get better care.
It is a sad state on current thyroid care and knowledge. The issue is not enough of us get involved and we are technically a medical minority that suffers in silence. Well I am not one to suffer silently. I will make myself heard and find everyone I can... and see that they get proper care.