When you think of how our bodies depend on those thyroid hormones, I wouldn't discount any symptoms! Also, anxiety goes right along with depression for me, so it's pretty much a given for a lot of people.
I don't think a TSI test was an option for me...I had TPO (negative), TGab (high), and TRab (in range). Even though my TPO was negative (which I think is the more common one for Hashi's) it was the TG that gave the diagnosis.
Were you hyperthyroid initially, and they are waiting until your thyroid is underactive (which it is, I don't know how your fT4 result can't yell this in their faces)? I wonder if you even went to a mediclinic or other doctor, if you could get a trial of meds? It certainly isn't going to make you hyper at a low dose to begin with, what are they so afraid of?