I'm assuming you were on NatureThroid or WP thyroid since those were the ones discontinued. I was on NatureThroid and very disappointed when they took it off the market.
Hmmm - it's odd your doctor won't write another script without making you go back for another visit. Definitely time to find a different doctor. I'm sorry I don't know anyone in your area, but can check around and see what I can find.
It's quite likely that the "mucous" is related to acid reflux/GERD, which is a very common symptom of hypothyroidism. Do you have any current thyroid hormone test results? If so, it would be great if you could post them, along with their corresponding reference ranges so we can see what's going on. Sometimes, we need more acid, not less. I take a couple of dill pickle juice when my GERD acts up, or take a peppermint oil pill, drink some ginger tea, etc.
Thyroid nodules are usually nothing to worry about and the thyroid is, typically, only removed if the nodules are causing trouble or are cancer (only about 5% of nodules are cancer). Have you had a recent ultrasound? If so, it would be good to post that report, as well