I hope you find out and let me know . I have been doing the same thing since 1980 when they removed mine. At one time they said the meds were not breaking down in my system. I have had so many changes I just cannot stand it any more I hope you can let me know.

Finally after many blood test an me doing my own research I got the Dr to put me on armour thyroid which hits two to three of ur thyroids. The Dr started me on a low dose which I felt a little better an started titraiting me up till we hit a dose that made me stable! I have been on it for two years now an about six months ago they had a shortage on the medication an I had to have the dr write a different thyroid medication after a month on the new medication I started wanting to eat more very sleepy ect. I went back an forth on. Meds for about 4 to 6 months an it messed my whole system up! I'm now back on the armour thyroid an feeling great! I highly recommend trying the armour thyroid if u have not yet!

Since it has been many months since you posted the question, you may be leveled out on your dose by now. The goal of thyroid hormone replacement is to suppress the TSH level (pituitary hormone) and to elevate the T4 and T3 to mid-range or above,
Your TSH at over "28." indicated overt (full blown) hypothyroidism. TSH elevates with hypothyroidism, while the thyroid hormones (T4 & T3) decrease to abnormally low levels. The average normal value at blood testing labs for TSH is 0.4 to 4.5 and your thyroid dose will need to get your TSH back down into this normal values range. Some doctors have a goal of suppressing TSH down to between "1.0 and 2.0" to successfully resolve hypothyroid symptoms of fatigue, weight gain, dry skin, constipation, etc...
I hope your Dr. has gotten you there by now!