Hello, May. Thanks for reaching out. Your symptoms certainly could be hypothyroidism, especially with the very high TSH and family history. A full thyroid panel would be helpful. This will help you rule out other problems as well.
However, even once tested, diagnosis is often delayed due to lack of full testing and very broad test result ranges. Your TSH of 7.5 is enough to indicate a serious thyroid problem. If blood tests aren't enough, an ultrasound of the thyroid can be used to diagnose Hashimoto's based on the presence of thyroid cysts or nodules.
Honestly, I have so many obvious factors pointing to thyroid disease (including a large cyst on my thyroid, and huge family history) and it took 15 years to get a diagnosis even after the cyst was obvious. I've struggled with my weight my entire life even as elite athlete.
Now, after 5 years, battling with doctors and medical systems, sickened by ineffective meds with side effects worse than this disease, I've come full circle and have gone back to trying more holistic ways to cure myself. I had become so sick from meds that I was bedridden for months. My bones are now extremely brittle (had a broken foot for over a year and a half still recovering, broke a tooth this week) and my immune system has been extremely damaged from the ineffective medications. So I basically have double the problem- the hypothyroid symptoms that persist even when the meds make the blood levels look perfect, and the side effects of enhanced hypothyroid symptoms, auto immune disease, bone loss caused by the meds. Ok, it's really like quadruple the problem.
Lastly, the meds are extremely difficult to regulate, so most people spend years trying to get the levels right and often never do. Likely because the meds are effected daily by diet, but take months to regulate through our detection methods of bloodwork. My point is that this system isn't very effective for thyroid disease treatment.
I encourage you to read through the many posts here to get a sense of what you're dealing with and how others have gotten relief using diet and nutrition, as well as lifestyle changes. There are so many things you can do to help thyroid health.
People here have been through it all and are willing to share their experiences of what works. Please ask many questions! Good luck!