Had VitD, B12, folate , ferritin tested? Not sure I'd bother about asking him about going gluten free, doubt if he has heard of it( and you have not been confirmed as Hashimoto's yet)... you can do your own thing re diet without his permission, and if you are diagnosed with thyroid autoimmune antibodies the NHS will never test it again. Important thing from blood results is to get appropriate 25 mcg levo increase and another test in 6 weeks( not 8,10 etc).
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