There are several conditions that affect the thyroid and affiliated thyroid stimulating hormones that can cause goiter and the symptoms you describe, not just Hashimoto's disease, but that is definitely one as well.
Goiter - MayoClinic.com
The lab values will definitely narrow it down and if in doubt, get a second opinion with a specialist, an endocrinologist. It is always worth it.
I hope you get the answer you need and help soon. Hang in there.