"There are many screening blood tests for celiac disease but the most sensitive and commonly used, whether symptoms are present or not, is the tTG-IgA test. All celiac blood tests require that you be on a gluten-containing diet to be accurate."
Your Free T4 and the prior Free T3 results just don't stand out as a hypothyroid problem. As mentioned your Vitamin D could be a bit higher, but B12 and ferritin don't seem to account for your symptoms. As Barb mentioned in the other thread you started, you should test for magnesium.
What time of day were you tested for the cortisol? Is the range you show time adjusted for the time of the blood draw?
My test report including FT3..
Date - 5 Mar 2016
FT3 - 3.31 (2.3-4.2)
FT4 - 1.36 (0.89-1.76)
TSH - 3.19 (0.5-6.0)
Additional tests (date 22 May 2016)
Calcium - 9.6 (8.5-10.1)
Cortisol - 14.55 (6.2-19.4)
Ferritin serum - 87.3 (21.8-274)
Hypothyroid patients should be treated based mainly on symptoms, along with Free T4 and Free T3 levels. It is too bad you were not again tested for Free T3. It is the most relevant thyroid hormone test since Free T3 correlates best with hypo symptoms. You need to make sure they always test for both Free T4 and Free T3 every time you go in for tests.
Do you have symptoms other than body aches and stiffness?
Your B12 is a bit higher than optimum, but not a concern since it does not build up in the body. Your D needs to be a bit higher, so maybe another 1000 IU daily would be adequate. You are also missing another important test, for ferritin. Ferritin should be at least 70 and some sources say 100. Have you been tested previously for ferritin?
I think you need to get the doctor to understand that due to the way ranges are established that many people find they need to be in the upper part of the ranges to get symptom relief. Also, people taking adequate levels of thyroid hormone frequently find their TSH in the low end of its range, or suppressed below range. Along with symptoms, that might be another indicator of being undermedicated. If your doctor has issues with all this, I suggest that you read at least the first two pages of the following paper and give him a copy of this paper and suggest that you would like to be treated clinically, by adjusting Free T4 and Free T3 levels as needed to relieve symptoms, without being constrained by resultant TSH levels. The doctor can confirm the validity of that approach by reading the paper. All the recommendations are well documented and supported with extensive scientific evidence.
http://www.thyroiduk.org.uk/tuk/TUK_PDFs/diagnosis_and_treatment_of_hypothyroidism_issue_1.pdf
In view of your symptoms, I also suggest that you should get tested for morning serum cortisol level. Also, it would also be good to test for Reverse T3 and also Free T3 from the same blood draw. Do you think that might be possible?
Please post your thyroid related test results and reference ranges shown on the lab report. What other symptoms do you have?