Read the rest of the earlier posts. I can speak only for Armour Thyroid (been on it since 1997) and it's gluten free. There are plenty of gluten free choices. I also recommend doing more research on thyroid meds outside of this site (we're really into Celiac Disease!)
I for one can multi task . I am "into" celiacs that is true but since other autoimmune diseases ( such as hashimotos ) go hand and hand with celiacs many of us have learn to multi task .
I can not recommend any of the "thyroid " sites for information . They are just plain scary .