Im sorry, I cant help with a doctor good thyroid doctors are few and far between and the best of them all has not long died.
You clearly have symptoms that could be ascribed to a thyroid condition and the gluten intolerance and vitamin D deficiency are often all part of the same picture.
Your results are only normal in the sense that they are within the reference ranges. Your TSH looks pretty good, but your FT4 is low in the reference range. The T4 converts to T3, which is the active hormone your body needs and if you are low in T4, which you are, you will inevitably be low in T3, which could explain your symptoms.
Im pleased to see you are working on the vitamin D. There will undoubtedly be a protocol in your area for getting this up to scratch, but it may well have passed your GP by. Because vitamin D is fat soluble, you need gelcaps or spray instead of tablets, and the equivalent of 2,00iu per day to raise your level steadily and keep it where it should be.
To find out what is really going on with your thyroid, you really need to get FT3, TPO and TgAB tested. The NHS can do all of these, but the lab may resist, whatever your GP says, so if necessary you can get them tested privately through Genova Diagnostics or Blue Horizon.
At the same time you need to get B12 and folate tested and also serum ferritin. B12 needs to be above 500 and ferritin above 70, although again your GP may say that they are normal if they come back within the wide reference range.
Thats something to be going on with, but think about coming to join us on the thyroid support thread and we will see if we can get to the bottom of this for you.