If they have not been done ......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 (our own or replacement ones) to work in our cells.
When you get results suggest you make a new post on here and members can offer advice 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.
As you have Hashimoto's then 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 of us 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
Best advice is to read as much as you can. Vitamin and minerals levels are very important, but standard NHS thinking, doesn't at the moment seem to recognise this.
You will see, on here lots of information and advice about importance of good levels of B12, folate, ferritin and vitamin D, leaky gut and gluten connection to autoimmune Hashimoto's too.