A swelling in the neck is a noticeable hint that something may be wrong. It can happen with both hypothyroidism and hyperthyroidism. The inflammation can also be the result of thyroid cancer, which is very easily diagnosed with a 6-minute ultrasound, Dr. Hall says, or nodules or lumps that grow inside the gland. Also, very low thyroid causes the body to retain water, she adds. Your hands, feet and legs can also swell.