I have hypothyroid(Hashimoto's)for 10+? years. I did Atkins diet and also reduced gluten. Since then, I have had to reduce thyroid meds. Their must be a autoimmune connection to gluten and maybe sugar. Wheat/gluten is a filler and probably toxic. Bread/Pasta has been called comfort food. Leads to wanting more pasta/bread. And I have read wheat protein breaks down similar to opiates. The first time I cut out carbs I was climbing the walls. I know it was the wheat withdrawals. Excessive Sugar can't be good for you either.
Do a test. Eat ONLY Sugar for a week, then bread for a week, then protein for a week.
I've found meat and whole foods/produce cooked or raw makes me feel great.
I stay away from bread, beans, and milk products(I'm less lactose intolerant since reducing gluten). Gas means intestinal distress.
Take only Synthroid. Don't switch back and forth from generic meds.
I like my TSH on the low end almost hyperthyroid.