The medicine levothyroxine is a substitute for the normal thyroxine produced in the body by thyroid gland. The medicine will reduce the symptoms of swelling of face  and weight gain etc. But the swelling in the neck may or may not reduce. Especially if it is filled with fluid which is called colloid. The swelling needs to be examined and evaluated. Apart from the thyroid hormone levels, which u have already done, get an ultrasound for the neck swelling and also a test called fnac which is done in the lab. A needle will be poked into the swelling and the material will be taken for examination. Depending on these tests the further treatment course will be decided. If u r having symptoms of breathing or swallowing difficulty or change in voice. Then show it immediately. Do not delay. U may require surgery in some cases.

You seem to be suffering from thyroid swelling secondary to decreased function of thyroid gland which is known as hypothyroidism. You need to take medicines advised by doctor. Probably swelling will reduce eventually