Thyroid gland can have many problems like under active thyroids, over active thyroids and thyroiditis which is inflammation of the thyroid gland. Feeling throat swelling can be due to thyroid problem but it requires differential diagnosis because many other factors can cause swelling of the throat and tonsils. So, alone feeling of swelling in throat does not confirm diagnosis of the thyroid problem. You should visit a doctor for differential diagnosis if you are suspecting a thyroid problem.