Suggest you ask GP to check levels of vitamin d, b12, folate and ferratin. These all need to at good (not just average) levels for thyroid hormones to work in our cells.
Vitamin D is apparently not really a vitamin, but a pre-steroid, good levels essential. Also been in the news recently, as we all tend to be too low levels due to modern lifestyle and not outside enough.
Vitamin c is good for stress and helping support adrenals.
Selenium may help reduce antibodies with Hashimoto's
Make sure you get the actual figures from tests (including ranges - figures in brackets). You are entitled to copies of your own results. Some surgeries make nominal charge for printing out. Alternatively you can now ask for online access to your own medical records. Though not all surgeries can do this yet, or may not have blood test results available yet online, but all should be doing this with couple of years.
When you get results suggest you make a new post on here and members can offer advise on any vitamin supplements needed
If you can not get GP to do these tests, then like many of us, you can get them done privately
Blue Horizon - Thyroid plus eleven tests all these.
This is an easy to do fingerprick test you do at home, post back and they email results to you couple of days later. Usual advice on this test, is to do early in morning, no food or drink beforehand (other than water) don't take Levo in 24 hours before (take straight after).
As you have Hashimoto's then (as Clutter advised in previous post) you may find adopting 100% gluten free diet can help reduce symptoms, and lower antibodies too.
Assume you know that Levo generally should be taken on empty stomach and no food or drink for at least hour after. Many take on waking, some prefer bedtime, either as more convenient or perhaps more effective. No other medications at same time, especially iron or magnesium, these must be at least 4 hours away