As you have coeliac disease, it's very likely that absorption of nutrients is affected. If nutrients aren't optimal then thyroid hormone can't work properly.
Do you have any test results to share with us? Please post them with their reference ranges so we can get a full picture. Ideally we need
TSH
FT4
FT3
Thyroid antibodies (to see if you have autoimmune thyroid disease aka Hashimoto's)
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