Did your doctor measure your thyroid antibodies? Did he actually feel your thyroid or send you out for an ultrasound? Autoimmune Thyroiditis (e.g. Hashimoto’s) is commonly linked to T1D and celiac disease.
Thyroid hormone replacement. That is what it is, a replacement. Do not think of it as a medication. I think once you start, you will be amazed at how much better you feel. The little symptoms you just simply got used to.