Have you looked into GoodRx? I don't use it for my thyroid meds, but it saves me about $140 every quarter on my vitamin B-12 injections.
You go online to the GoodRx website, put in your zip code and the drug you're interested in, along with number of dosages and it comes up with the price at a variety of pharmacies. You choose which one you want, print a coupon and take it your pharmacy when you get your script filled.
Not sure how it would compare to Walgreen's discount club, but it might be worth checking into.