Yes they ARE related, some say untreated celiac can lead to thyroid dysfunction. My daughter was diagnosed last month with vague symptoms but some you describe, some bloating, fullness etc.. the gluten free diet has really helped alleviate it. She tested positive but still had to have a endoscopy with biopsy to confirm. The villi in the small intestine become damaged and you can't absorb your nutrients. This will lead to vitamin deficiencies,anemia, osteoporosis,and other organ dysfunction or worse if you keep eating gluten. There are many sites out there to help,you need your vitamin levels checked also. I have a combo of Graves and Hashi's although was treated for Graves. I have been trying to unravel this auto immune thing with me since my Mom doesn't have a thyroid disorder,as far as I know(had tests, she's 86) but has had signs of celiac for about 30 years. We will both be tested sooner or later although I don't really have symptoms but I have researched it a lot and supposedly, you don't need to have a lot of classic symptoms at all to have it. Even joint pain can be a symptom,or depression and anxiety which are thyroid symptoms too. I hope you get an answer soon but try the diet for 2 weeks (you can find a list of no no foods on the internet) but mostly wheat, barley and rye so NO bread,baked goods,all that carb stuff except for rice. They sell a lot of gluten free foods now and there are foods that are naturally gluten free. You can start out with just meat, potatoes, rice and fruit at first, then add more as you go along. It's hard at first but if you know what to avoid it's not so bad and you won't feel sick anymore, you'll be healthier and you won't be damaging your intestines. Good luck to you!