Hi, maybe I missed it, but did you get your blood checked on antibodies?
Anti-TPO & anti-tg I mean.
These are the ones that need to be checked if you are likely to have hashimoto's.

(I have hashimoto's for 11 years now)

Btw, not to put your down, but losing weight or a change in BM becauce you start levothyroxine doesn't mean you're hypothyroid; it would happen to almost anyone.
I do however see why you think you have hashimoto's; especially your family members having a-i diseases as well. Did your sister was hyper because she had graves disease?

As for your blood results, this may be another sign. If i recall correctly (mind, it has been a while since i was "into" the thyroidworld), it sometimes happens when a patient finally starts levorhyroxine the thyroidlevels become even more hypothyroid.

My advice is to check the antibodies, but also be sure you do not overdose! Take it slow, checking your blood regularly.
I am not sure why, but whenever it's about diabetes doctors are way more helpful, they let you check your glucose very often. If you do however ask to check your thyroidlevels they tend to be less eager. That's my experience anyway. It seems like loads of them underestimate the immense effect an unbalanced, sick thyroid can have.
Wish you all the best.

By the way, I don't know why you see a shrink, but thyroidproblems very often cause mentalproblems too!