I sure do understand why you would be so concerned, after your prior experience.
A couple of things to clear up. Synthroid is synthetic T4. Synthroid is just a brand name, like Levoxyl and Levothyroxine. The only difference among them is the filler/binders/dyes used to make the different tablets. Also, when I mentioned revising your med/dosage, I did not mean increase the Synthroid. In actuality you could slightly reduce your Synthroid dose and add some T3 to raise your Free T3 levels into the upper half of the range, and then adjust further to relieve hypo symptoms.
Further, TSH levels mean very little when taking thyroid med. In most cases, TSH becomes suppressed below range when taking adequate thyroid med. Many doctors don't understand that and if it occurs they want to reduce meds based on interpreting a suppressed TSH as being hyperthyroidism. In reality it is hyperthyroidism only if having accompanying hyperthyroid symptoms due to excessive levels of Free T4 and Free T3. I mention this only to make you aware of it since increasing your Free T3 level may suppress your TSH. You can read about this in Rec. 10 on page 14 of this link. My own TSH has been suppressed well below range for for 30-35 years without ever having hyper symptoms.
http://www.thyroiduk.org.uk/tuk/TUK_PDFs/diagnosis_and_treatment_of_hypothyroidism_issue_1.pdf
As for being within "normal" limits, that doesn't mean adequacy. The ranges are far too broad due to the erroneous methodology used to establish ranges. The all important objective for treatment with thyroid medication should be symptom relief, not just test results, and especially not TSH levels. You can read about this in Item 4 on page 5 of the above link. In addition, every one can have different levels at which they feel best, since there are many other processes and variables that affect tissue thyroid effects (symptoms) See also Fig. 1 in the link.
Can after a total thyroidectomy and radioactive iodine 35 years ago could it grow back or thyroid tissue? I just looked at CT scan from 09/14 that report says " minimal remnant thyroid tissue". CT scan 12/16 report says "thyroid gland within normal limits". Hmmm? I have a history of treating my MS with interferon beta 1-A weekly for 15 years. Was very successful of keeping progression slow but subsequently I developed non Hodgkin lymphoma and can no longer do that.
Besides Synthroid there are many generics like Levoxyl, or Levothyroxine. All are synthetic T4 hormone. Then there are the desiccated (porcine) thyroid meds like Armour Thyroid, NatureThroid, and Westhroid, all of which contain both T4 and T3. And then there are the synthetic T3 meds like Cytomel, and generics.
Your Free T4 is at 70% of its range, while your Free T3 is only at 16% of its range. This imbalance is indicative of poor conversion of T4 to T3, likely due to taking only T4 med, correct?
Many of us have found it best for Free T4 to be at least mid-range, along with Free T3 to be in the upper half/upper third of its range, or as needed to relieve hypothyroid symptoms.TSH means very little when already taking thyroid med.. In fact, the majority of people have suppressed TSH when taking adequate thyroid med. Note that would not mean hyperthyroidism, unless there were accompanying hyper symptoms due to excessive levels of Free T4 and Free T3. A good thyroid doctor will treat a hypothyroid patient clinically by testing and adjusting Free T4 and Free T3 as necessary to relieve hypo symptoms, without being influenced by resultant TSH levels. Symptom relief should be all important, not just test results, and especially not TSH results.
So you need your med revised. What med/dosage are you taking now?
T3 reference range = 2.3 - 4.2
T4 reference range = 0.8 - 1.8
TSH reference range= 0.40 - 4.50
You said you have no signs of being hypothyroid, yet you mentioned several: night sweats, hives (could be related to the antibodies of Hashi's), and fatigue. Along with a Free T3 of 2.6, I expect that your thyroid medication is inadequate. What are the reference ranges shown on the lab report for the T4 and T3 results?