I don't understand why you had parathyroids removed because of Hashi"s. Although the parathyroids are right behind the thyroid, they are not related to each other in any way, except by their names and location; they serve totally different functions in the body. Many people have the thyroid removed and the parathyroids remain intact unless there is a specific issue with them.
We have 4 parathyroids - one behind each quadrant of the thyroid gland; did you have all 4 of them removed? I think it's very rare to have all 4 of them removed, particularly because of Hashi's.
That said, hypothyroidism "can" cause anxiety. I'd recommend that you check out the thyroid forum and ask your question. You should have your latest lab results and post both the FT3, FT4 levels, along with the lab ranges, since these vary from lab to lab, so must come from your own report.
I had my thyroid removed as well about 16yrs ago. I have been on Levo for that long as well.
I have never experienced anxiety. I know my TSH level is always kept at under 1.0.