A goitre is just a swelling of the thyroid. I had a little trouble swallowing when mine was swollen.
Get you a glass of water, stand in front of a mirror, take a drink hold the water in you mouth, hold your head up, swallow the water while looking in the mirror at your thyroid. You will be able to see it move up and down.
It surrounds your windpipe. When I had a goiter, it seems like my right side was a little larger than the left side.