Quote: they started me on thyroid when my numbers were high
I assume you mean your TSH was high, not your T4? (TSH is a measure of the signal from the pituitary to the thyroid, telling it to make more thyroid hormone. Usually, TSH goes up in response to a low T4 (low circulating thyroid hormone).
Being on thyroid suppression for a goiter does not necessarily mean you will have to be on it forever. However, the goiter may grow if you go off. If your thyroid was low to begin with, and that was the cause of the goiter, then you might have to stay on thyroid simply because your thyroid may not recover normal function due to whatever underlying process was making it low in the first place. There are some other inherited defects of thyroid hormone processing that can lead to goiter, and with your dad's history, it is possible you have something like that.