I also have Hashimoto's. It took me 12 years to get diagnosed. My levels were always well within the "normal" range. I finally went to a Dr. that did a thyroid antibody test. My numbers were through the roof! Hashimoto's is an autoimmune disease as is Celiac. Many people that have one autoimmune disease often have another. Find a good Endocrinologist and have the proper tests run. When you get your medication to the right levels symptoms go way down. I have gone down 2 sizes as well. Good luck.
It is not surprising at all that your dogs are healthier. Dogs are not ment to eat grains. Many dogs have wheat allergies. Our kids can feel they are not alone because even their dog can't eat wheat. We feed our dogs Canadae. There are others that contain no grains too.