When I first went on synthroid, a large amount of my hair starting falling out or getting thin and brittle. When I switched to armour, this fixed it almost immediately. May be worth discussing with your doc.
Would test to make sure the thyroid levels are stable (TSH 0.5-2.5). The hair does not always grow back the same way after chemo. There are hair/nail vitamins that can be taken -- they are available over-the-counter -- it sometimes helps.
The thyroid medication itself would not cause the hair problems -- but thyroid imbalance can contribute (ie if the levels aren't on target).