Your ferritin is too low for your thyroid hormone replacement to work well. Optimal range is 70-90 so I would suppliment iron to get to those levels. Without good ferritin levels you won't convert or utilize thyroid hormones effectively. Be sure to take your iron at meals with plenty of vitamin C and avoid calcium, tea, coffee or thyroid hormones when you take the dose.
I can't say for sure if going gluten-free is going to help you or not. Generally you need to stay on the diet for several weeks or at least a couple of months to see if it makes a difference. But discontinuing the meds and a return of the symptoms seems to point to a intolerance to yeast or something else going on. Also when starting of stopping medications or suppliments it's a good idea to just do one at a time so you can pinpoint which one is helping or hurting you.