the normal TSH does not mean it's not thyroid enlargement or inflammation.
Would test blood for T4, T3 and ESR. Other useful tests may be thyroglobulin antibody and level as well as TPO antibody.
An ENT evaluation is likely the best next step. A CT scan of the neck will demonstrate any compression on the trachea (windpipe). Flow-volume loop (lung function tests) can be ordered to document any change in air movement. These tests could be ordered by a general doctor but if abnormal and ENT or thyroid specialist would help address treatment options (medications vs surgery, etc). If the breathing problem increases in the meantime, then go back to the ER.
Don't want to but in, but if he is still having problems breathing and they did not give you anything to change this, if it was my child I would call my primary immediately and if he didn't answer immediately i would be at a hospital based emergency room. it is friday afternoon and reaching doctors can get harder over the weekend.
It is not like you can wait around when you are not breathing.
Dr. Lupo may have other suggestions, but I don't think I would wait for that either.