hair loss from hair color?

I have been losing quite a bit of hair in the last three months. I had originally lost hair a few years ago and discovered I had an underactive thyroid but after a few years the hair loss started again. My dr. put me on T3 topical cream once a day and the hair loss still continued.  I have stopped both medications as a test and have noticed less hair loss. I have been taking chlorella which is a form of algae and wonder if the iodine in the algae combined with the medications was too much for my thyroid. I had a friend that suggested that the hair loss could be caused from coloring my hair. I do not bleach it but just use it to cover gray.