Does this seem like a possible autoimmune thyroid disorder or something else?

[Pandafluff]

This is something I've been struggling with for about 4 years now. I'm a 30 year old female. Firstly I will list the most notable symptoms and then my lab values over the years...

Extreme fatigue
Trouble concentrating/memory issues
Some hair loss (thankfully I still have lots)
Dry, itchy skin
Periodic unexplained weight gain
Trouble maintaining weight/losing weight
Periodically brittle nails
Generalized Anxiety

Lab results:

TSH tested 5 times over the past 4 years

-Current TSH value: 2.27, reference range 0.30 - 5.50 mU/L

-Lowest recorded TSH value to date: 1.52,  reference range: 0.30 - 5.50 mU/L -  Jan 23, 2016 - (I felt pretty awesome here but for a few minor things)

-Highest recorded TSH value to date:  4.22, reference range: 0.30-5.50 mU/L - May 22, 2015 - (I felt awful here)

Other two times it was tested: 1.71 and then 2.39

Thyroid Peroxidase Antibodies:
Typically hovering around 35. Lowest so far was 28, highest so far was 36.
Currently at 35, reference range < 35 kU/L

Thyroglubin Ab: <10, reference range <40 IU/mL (tested twice but never got the second result)

Thyroglobulin: 9.8, reference range 600 ug/L, consider
test for iron overload (transferrin
saturation).
^this is current, historically it has always come back lower.

And now the weight problems:
My diet is pretty consistently healthy, aims for adequate nutrition and low calories, low carbs, low sugar. I recently found out I'm very likely both gluten and lactose sensitive so these are currently in the process of being cut out.
I have not been able to do very much exercise in the last year and a half due to extremely low energy and what seem almost like arthritic flare-ups, so most of my weight management is coming from calorie cutting at the moment (but staying between 1200-1500 calories per day). I've noticed if I go over that I gain weight pretty fast. The only time I've really been able to lose any amount of weight in the past rather than keep it stable was through walking literally everywhere, plus getting in 2-3 straight hours of cardio (just nonstop fast paced walking so I don't hurt myself, I've had past injuries and some weird arthritic stuff going on) and even some physio throughout the week. I think that's a bit extreme and obviously don't have the energy for it anymore. I'm 5'4" and 150lbs at the moment, trying to muster the energy to get back into a good fitness routine but I feel like I need to sleep constantly.

I am strongly suspecting thyroid issues (possibly Hashimoto's because of the autoimmune component). Autoimmune diseases do run in my family, but since my family is long gone I can't get an accurate history.

Possibly relevant: My mom (who is still around in another province but also can't get a diagnosis because of language barrier issues) has mentioned having thyroid issues when she was younger, but in eastern europe... Apparently they had her drink some sort of iodine thing to partially kill off her thyroid a few years before she had me.

I can barely get my doc to talk to me and discuss this stuff with me.

[Pandafluff]

ignore this post, it seems that for some reason part of the post is missing valuable info and something else got spliced in