There is a very active thyroid group on a low-carb board. It seems like a lot of people with an underactive thyroid have difficulty with carbs and they seem to do well on low carb diets. Another thing I've seen mentioned is that your medication might not be optimized. If you are still having symptoms - low energy, hair loss... you might want to talk to your doctor about your med levels and especially your T3 levels.
I was just diagnosed with hypo about 2 weeks ago and so I'm actively researching! I'm hoping that losing weight will be easier when my medication is at the correct level. Good luck! - Jane