Before further discussion, we need to clarify your med dose. Is it 25 mcg? Also, we need the reference ranges shown on the lab report for those results. What was your cortisol test result and reference range? You said you had Hashimoto's. Was that confirmed by testing for the autoimmune antibodies associated with Hashi's? Why did you get new lab tests done after one week?
My Hashi's fluctuated badly with toxic mould. I had magnesium deficiency from insulin resistance, sugar, stress (notably after surgery) and high doses of vitamin D. Low magnesium is also one of the possible causes of low potassium. Cortisol is the stress hormone.
Time of day tested:
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.
And an article that lists 15 other reasons...
About Guide - Reasons Why Your TSH May Be Fluctuating...
"Change in Dosage - changing your thyroid medication may change your TSH.
Potency Fluctuations in your medication
Lab changes or mix-ups
The timing of when you take your pill
Starting or stopping a high-fiber diet
Starting/stopping calcium or iron supplements
Eating too many soy products
Eating too many goitrogenic foods, which include Brussels sprouts, rutabaga, turnips, kohlrabi, radishes, cauliflower, African cassava, millet, babassu (a palm-tree coconut fruit popular in Brazil and Africa) cabbage, and kale
Change of seasons -- TSH can rise in the colder months
Certain prescription drugs
Stress or illness
Progression of your thyroid disease."
I think the starting point for you should be that you have previously been diagnosed as having Hashimoto's over 5 years ago. As a result the antibodies have been continually attacking your thyroid gland until it is destroyed. As this is happening the ability of the gland is diminished, resulting in less output of thyroid hormone. This then causes the pituitary to produce more TSH, in an attempt to stimulate more production of thyroid hormone.
Rd_Star gave you lots of possible causes for the variability in lab test results. I see no need to focus further on why there is variability. Rather we need to focus on the whole picture and assess your thyroid status. To do that the starting place should always be an evaluation for those symptoms that occur more frequently with hypothyroidism. When you look at a list of some of the most common hypothyroid symptoms (slow reflexes, dry skin, coarse skin, puffiness, lack of sweating, with gain, paraesthesia, cold skin, constipation, hoarseness, hearing loss) you have a few related symptoms from that list and if I look hard enough at an even longer list I can find a few more. However, there are some that don't seem to fit with hypothyroidism.
Looking at your test results, I don't pay much attention to TSH because it is affected by so many things that at best it is an indicator only when at extreme values. Your Free T4 was at 25% and 41% of its range, for the two dates respectively. Your Free T3 was at 28% and 4% respectively. Compare that to the words of an excellent thyroid doctor.
"The free T3 is not as helpful in untreated persons as the free T4 because in the light of a rather low FT4 the body will convert more T4 to T3 to maintain thyroid effect as well as is possible. So the person with a rather low FT4 and high-in-range FT3 may still be hypothyroid. However, if the FT4 is below 1.3 and the FT3 is also rather low, say below 3.4 (range 2 to 4.4 at LabCorp) then its likely that hypothyroidism is the cause of a person's symptoms."
Based on all this I would say you need to increase your thyroid med dosage. As to what levels are required, the following is a conclusion from a recent, excellent scientific paper. 'Hypothyroid symptom relief was associated with both a T4 dose giving TSH-suppression below the lower reference limit and FT3 elevated further into the upper half of its reference range." To achieve that level of Free T3 will also require the addition of T3 to your med.
In addition hypothyroid patients are frequently deficient in Vitamin D, B12 and ferritin, so those need ot be tested and then supplemented as needed to optimize. D should be at least 50 ng/mL, B12 in the upper end of its range, and ferritin should be at least 100. All three are very important for you.
Although the morning serum cortisol test is for total cortisol and is not as revealing as a diurnal saliva cortisol panel of 4 tests for free cortisol, your cortisol test is in a good area of the range. So what I suggest is that you get your doctor on board with additional thyroid med, including a T3 med, and get your levels consistent with the info above. Also get your D, B12 and ferritin optimal and allow a few months for your body to heal and get the most from all this and then see how you are feeling at that time. If there are other issues at play, they will be easier to identify at that time.
If you want to confirm what I say, please click on my name and then scroll down to my Journal and read at least the one page overview of a full paper on Diagnosis and Treatment of Hypothyroidism: A Patient's Perspective. You can also make good use of the info there with your doctor, if there is resistance to doing what we have discussed here.