Untreated coeliac is thought to cause other autoimmune disorders such as hypothyroidism so I expect you've been coeliac for quite some time and this may have cause the thyroid issue or impacted it in some way.
It will take a while to get your thyroid replacement dose up to the right amount as you have to increase and then wait 6-8 weeks at least to retest and see if you need more so it will just take some time. Many Gps are not great at medicating thyroid so you may want to post your blood test results on here for further advice to see if optimally medicated. If you do not have thyroid antibodies and it is being caused by nutritional deficiency and other ongoing issues with untreated coeliac, you might find your thyroid function improves after going gluten free although this may not happen.
In regards to coeliac - this is actually great news as it is the one thing that is easily and perfectly treatable! You would have had this for a while so now you can resolve your health issues. You have to read up on cross contamination and even do things like buy a new toaster - read up on coeliacuk website, they have a lot of useful info on there. You have to be 100% gluten free to get rid of your symptoms. You should get further coeliac antibody tests to see if your new diet has lowered them enough or whether there are still areas you need to look at. It can take at least six months for your stomach to heal and for some of the symptoms and sometimes even a year or longer for full recovery - your immune system will remain triggered in your system for 3-6 months so even having one can of beer every three months is enough to keep you very poorly. However, you will find your health improving over this time.
If you do it properly, you should see massive improvements in your health and even things disappearing that you've ignored for a long time and thought was nothing - aches and pains, indigestion, teeth issues, fatigue and brain fog, eczema/rashes and so on- it can effect every area in your body. For example, when I went gluten free, this was the first time I realised I had ankles lol! I always had really fat lower legs and thought that was the way they're built but it turned out to be water retention all those years
If you are struggling to figure out what to eat, I found sticking to simple food in its most natural form and unprocessed easier until I could get a better grip of reading labels and knowing more about it. Things like rice/potato/certified gluten free oats, meat, dairy, fruit, nuts, seeds and nuts were all I ate at first until I could get my head round it. Once your energy starts to return, you will be better placed to think more about it. Read up on coeliac uk, the more you understand and read, the better position you will be in to get better
You must get all your nutritional levels tested and treated as you will have most likely have deficiencies - things like iron/vit b12/folate/vit d and many more. Again, post them on here for advice.
You should also have a dexa scan to check bone density as your bones are likely to have suffered from this and they treat to improve this. This and the nutritional testing should be offered as standard to anyway diagnosed with coeliacs anyway.
Hope you start to feel better soon