I don't know how may other peopole have this, but for what it's worth, I have had a hoarse voice and sore throat ever since I started getting hypothyroid (that was 3 years ago). If I talk too much I lose my voice completely.
I don't have a goitre and I don't have Hashis either.
Based on my experience, I'd say yes, although there are other possibilities that come to mind. Do you have any allergies?
Are you still somewhat hypo? What thyroid test results can you post, along with their reference ranges shown on the lab report? Do you have other hypo symptoms? Maybe if we see those results and any symptoms you seem to have we can assess the adequacy of your testing and treatment.