If after you get vitamin levels optimal and Levo dose increased so that TSH is around one and FT4 towards top of range, if FT3 still remains low then you may, like many with Hashimoto's, benefit from addition of small dose of T3
You might also consider DIO2 gene test
Available via Thyroid UK or Blue Horizon
Were you tested for coeliac before going gluten free?
B12 needs to be at least 500 and nearer 9000. And 800iu is a very low maintenance dose. You could read the NICE guidelines re a booster dose to improve it or just buy your own as they are relatively cheap.
Look at SeasideSusie's posts for more about vits etc
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