There are lots of drugs beside anti-thyroid drugs that can cause hair loss. This article lists some of them, in case you are taking any other meds.
https://www.dovemed.com/diseases-conditions/drug-induced-alopecia/
I was only on methimazole for six months before choosing thyroidectomy. Maybe wait to see how it goes for a bit longer if you are trying for remission before choosing definitive treatment like RAI or thyroidectomy. I chose TT because I had the eye disease too.
