Endocrinology Questions? Ask an Endicrinologist for Answers ASAP
As long as you are seeing an endocrinologist for your management of your thyroid, some patients do take both T4 and T3 at the same time, though this is controversial.
a normal TSH is 0.5 to 4.5 or 5.0 depending on the lab
the fact that your TSH is going up suggests that your're not being properly supplemented.
It would be best recommended that you be treated with levothyroxine and your levels evaluated systematically as you are titrated up or down from the initial starting dose.