I personally believe that Mercury does in fact affect the thyroid in the form of TPO antibodies.
I was diagnosed with Hashimoto's disease about three years ago and had TPOab's in the 180 range, with the acceptable range being <6. I had Mercury Amalgam fillings in my mouth for about the last 25-30 years, and promptly had them removed by a qualified dentist. Notice I said qualified because if they are not careful, you can wind up in worse shape than before you walked in there office. Do your homework.
Anyways, 3 months after their removal my TPOab's began to drop, and today they are down to <6.
Still have other issues, but I would recommend you get a good thyroid panel done that includes checking for thyroid antibodies.