What happens when you get a goiter? Does it go away completely if treated for hormone problems?

Depends. Depends on type of goiter, thyroid function and treatment. A treatment that frequently (but not always) causes significant shrinkage is radioactive iodine for an over active thyroid.
Not necessarily. It depends on the reason for the goiter. If you are also hypothyroid than thyroid replacement might cause a decrease in goiter size. See a thyroid doctor.