I agree with the thyroid test, both of them. AND you should have one done one week and then have another test the next week to compare the 2 because the thyroid is a tricky little booger and it can really mess with your whole body system. You may want them to throw in an iron test as well. Maybe your not absorbing iron as you should. Alot of people that have hypothyroid(like me) are anemic too. At least that's what my Endo told me.
If those come back fine, I'd go for the sleep study and then the gluten test. I hope you get to feeling better.