Have you had your TPO and Tg antibodies tested? If not, then I suggest asking your dr to get that done. Its possible, by lowering your dosage of Synthroid, that your antibody count (if you have antibodies) has been rising and causing nodules. Multiple nodules are very common with Hashimoto's, although that's not the only cause.
While the statistics say there's only a 5% chance of nodules actually being cancer, its something to rule out. Depending on the size of your nodules, your dr will either want to monitor them or send you for an FNA. Thyroid cancer is very slow-growing so, in spite of how badly we want to know, there really isn't a reason to rush.
Something else to think about is that hypoT can cause low stomach acid, which in turn can cause acid reflux. While you may not notice obvious signs of reflux, it can cause problems like hoarse voice, chronic cough, trouble swallowing, and a feeling of pressure in the throat. Its best to get this looked into as well.
The thyroid forum on this board has lots of excellent info, as well as folks who have been through all sorts of thryoid stuff and are eager to share the benefit of their experience and reading. Feel free to wander over there. You'll be welcome.