Tirosint is reported to absorb better than other T4 meds. In addition the Armour dosage of 45 mg is a significant reduction from the 88 mcg of Tirosint. Most doctors use the standard conversion tables showing that one grain of desiccated thyroid med like Armour is equivalent to 100 mcg of T4. That is incorrect. The ATA/AACE Guidelines for Hypothyroidism recognizes scientific studies that concluded that T3 was about 3 times as potent as T4. One grain of Armour (60) mg contains 39 mcg of T4 and 9 mcg of T3.
Accordingly one grain of Armour would be equivalent to only 66 mcg of T4 (39 mcg of T4 plus 9 mcg of T4 times 3 equals 66). Thus 88 mcg of Tirosint would be equivalent to at least 1 1/3 grains of Armour, not 3/4 grain.
So the increased TSH is due to the reduction in thyroid med dosage. By the way, TSH should not be used to determine thyroid med dosage anyway. That is because going from a continuous very low flow of thyroid hormone in the untreated state to taking replacement thyroid med once a day, significantly changes the equilibrium among TSH, Free T4 and Free T3. When hypo patients' thyroid med is being adjusted just to return TSH within range, the patient is typically under-medicated. A recent scientific study concluded that, "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. " This is what a good thyroid doctor will do for a hypo patient.
Another thing to note is that hypothyroid patients are frequently deficient in Vitamin D, B12 and ferritin, so you should make sure those are 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. If you want to confirm all this, click on my name and then scroll down and read my journal.