Welcome to our forum and your story is familiar. You now have to take your own health into your own hands and become well.
You don't say whether or not you are on thyroid hormone replacements but you state you have Hashimoto's. The commonest form of hypothyroidism. Many doctors only look at the TSH and if it hasn't risen sufficiently will not provide levothyroxine. In the UK the guidelines state that we have not to be treated till TSH is 10 and in other countries it is around 3 that you will be prescribed.
You have to have a FullTthyroid Function Test. If GP wont do all of them you can get a private test. Your GP should check Vitamin b12, Vit D, iron, ferritin and folate.
Blood tests have to be at the very earliest possible, fasting (you can drink water) and if you are on thyroid hormone replacements allow a 24 hour gap between last dose and test and take afterwards.
If you are on not on any thyroid hormone replacements at all but have thyroid antibodies, despite TSH, you should be prescribed levothyroxine.
FTFT - TSH, T4, T3, Free T3, Free T4 and antibodies.
Always get a print-out of your results and the ranges must be stated as labs differ and ranges make it easier to coment. Post your results on a new question.