Yes, here in the states the TSH seems to be rather important also.
Sometimes you can find a doctor that will watch the Ft4 and Ft3. I know it can be so hard. "The TSH is not a good test for severity of tissue hypothyroidism." You might want to see if you can find some proof to show the doc about TSH. Especially after you are taking thyroid replacement, the TSH is so useless.This keeps many people sick with higher cholesterol levels, depression, high bloodpressure and the list goes on.
I know that it does take awhile to get well once on thyroid medicine, and the waiting and suffering can be so very hard to deal with.
Yes, I believe what you have is a goiter. This is just another name for swollen thyroid. When your thyroid levels become normal for you, the swelling should go down. If you have a thermometer, check and see what your temperature is. In the morning before getting up it should be between 97.8 to 98.2. In the afternoon, it should be getting up around 98.6. A mercury thermometer is more accurate, but are hard to find these days, since they are being banned.