Levoxyl and Hair Loss

I have a hypo active thyroid and have been on levoxyl since I was 43. I have never had any side effects at all and I'm now 54. My thyroid levels have been fine through having three children, but in the last couple of years have gone up and down a bit. Now, my level reads fine with my current level of levoxyl. In the last year or so, though, I've been losing a lot of hair, to the point of having about half of what I used to have. I did go through menopause at 50, but this hair loss started three years after that. I recently read about taking a combination of iodine and iodite and want to know if it's ok to take this with levoxyl. Advice? Thanks.