Celiac and Hashimoto's are 2 separate conditions, so if the rashes and some of the other symptoms were caused, strictly, by celiac, you won't have to deal with those again, as long as you stay off the gluten...
The only way you can know whether you really need the synthroid is by keeping a close watch on your FT4 and FT3 levels and if they stray below the mid range points and you have symptoms of hypothyroidism, you'll know you need it. Don't ever just go by TSH... always make sure it's Free T4 and Free T3.
I'll look forward to seeing the correct reference ranges...
The range for the Free T4 looks close to what we often see, however, could you call the doctor and find out about the range for the Free T3? It look pretty strange.
At any rate, your Free T4 is on the floor of the range and your Free T3 is not far from it. That means you're still basically, hypo. Most of us find that we feel best with Free T4 about mid range and Free T3 in the upper half to upper third of its range.
I'm guessing your meds were stopped, based on your TSH level, however, for many people on thyroid hormones, TSH often becomes irrelevant... for instance, my TSH has been at < 0.01 for the past 8 yrs, even when I was very hypo. For many of us, TSH does not reflect thyroid hormone status and judging from your actual hormone levels, you're one of those.
If you have confirmed Hashimoto's, you will eventually, need thyroid medication, as there is no cure for Hashimoto's and it will eventually destroy your thyroid. Going gluten free can't stop that, however, if you have celiac, without a doubt, you need to be gluten free.
Many people find that they lose weight when they go gluten free, because they stop eating all the bread and other things made with flour that causes weight gain...I lost 26 lbs by eliminating a lot of that from my diet, but didn't stick with it... congratulations on reaching your goal weight.
What are the reference ranges for the Free T4 and Free T3? Your Free T4 still looks horribly low, as if you're still very hypo.
When in September did you go off the med?
It's never been proven that gluten affects thyroid hormones levels at all, so it's unlikely that going gluten free has anything to do with your thyroid levels.
With Hashimoto's, it's very possible to swing from hypo to hyper and even have periods of normal in between... I'm just not sure you don't need the med.
The reference ranges for the FT4 and FT3 will help determine that.