Gluten Free Medication

I am still very new to meds, just finished my first bottle. I have celiac so I need medication to be completely gluten free to ensure I am not damaging my intestines. So, I've been taking Synthroid because I have confirmed that it is definitely gluten free. But, it is very very expensive. My insurance is not fully covering it. It was $55 last month. This month I got it down to $36 with coinsurance from the manufacturer. But, that is still a lot for money every month. So essentially I have two questions

1. Does anyone have any experience with a generic that is definitely gluten free? If so, what is the manufacturer and can I request a particular manufacturer?

2. Does anyone have any experience getting Synthroid cheaper? Did you fight with your insurance company or find a good coupon?

Thank you very much! I hope this was the right thread to ask it in. I was unsure if I should ask here or in celiac subreddit.

My pharmacist has been very unhelpful he said the gluten in the generic is "too little to hurt me". Sure if it was a short term medication, maybe. But every day it's going to build up! Ugh it's so frustrating. My endocrinologist is supportive but doesn't really know how to find out what is gluten free or not. And my GI doctor is terrible so that's also not an option lol.