It's unfortunate that you didn't do the Free T3 every time you did the TSH and Free T4, since Free T3 is the active hormone that's used by nearly every cell in your body. If we had Free T3 results for each set of tests, we'd be able to see if it were coming down, as well as the Free T4, but I think we'll assume it is...
That said, your latest Free T4 is very low in the range, at only 20%. Most of us feel best with Free T4 about mid range and Free T3 in the upper half to upper third of its range.
You're correct that TSH can fluctuate - not only from stress, but from a variety of other things as well. It can actually fluctuate by as much as 75% over the course, of a single day, so it's always best to try to be consistent in the timing when you have it tested. TSH tends to be higher in the morning than later in the day, so if you can tell us what time these tests were done, that might be helpful.
I'm not sure about your antibody tests. Are the TAB(glu) Thyroglobulin Antibodies and TAB(per) Thyroid Peroxidase Antibodies? If so, just for information, the proper abbreviations are TgAb for Thyroglobulin Antibodies and TPOab for Thyroid Peroxidase Antibodies.
Even though your antibody tests are negative, you could still have Hashimoto's, as some people are diagnosed, based on ultrasound results that show specific characteristics. You should ask your doctor to order a thyroid ultrasound. An ultrasound will also tell you whether you have nodules and/or a goiter (swollen/inflamed thyroid).
Last, but not least, could you please list your symptoms.
When I had normal thyroid function my TSH was always hovering around 1.4 to 1.6 mU/L (many TSH tests over the decades). When Hashimoto's thyroiditis showed up my TSH finally rose into the 2's and both thyroid antibodies - TPOAb and TgAb were positive. My endo tested me for celiacs too. I was thankfully negative. I already have 4 autoimmune diseases and no more need apply thank you very much!
The August 2012 study entitled "Clinical Significance of TSH Circadian Variability in Patients with Hypothyroidism" (Sviridonova MA, et. al) showed an average morning TSH level in the subclinically hypothyroid group was 5.83 mU/L and in the afternoon was 3.79 mU/L; 73% TSH circadian variability.
The average morning TSH level in the hypothyroid group taking levothyroxine was 3.27 mU/L and in the afternoon was 2.18 mU/L; 64.7% TSH circadian variability. Morning: 8 - 9 am. Afternoon: 2 - 4pm.
"The prevalence of autoimmune thyroid disease in patients with celiac disease is four times greater than that in the general population, and this may be due to the common genetic predisposition" - Beyond Celiac - Celiac and Thyroid Disease