Do you have results for TSH, FT4 and FT3. Do you also have high thyroid antibodies? You need to know. Did GP ever test these? If not ask that they are tested.
If antibodies are high this is Hashimoto's, (also known as autoimmune thyroid disease). About 90% of hypothyroidism in UK is due to Hashimoto's.
Hashimoto's very often affects the gut, leading to low stomach acid, low vitamin levels and leaky gut.
Low vitamins that affect thyroid are vitamin D, folate, ferritin and B12. Important to test these. If they are too low they stop Thyroid hormones working. Have these been tested, if not ask that they are. Always get actual results and ranges.
Post results here if you have them.
If you have Hashimoto's then hidden food intolerances may be causing issues, most common by far is gluten. Changing to a strictly gluten free diet may help reduce symptoms and eventually start to lower antibodies. Very very many of us here find it really helps and can slowly lower antibodies, improving symptoms