If you feel more comfortable with a second opinion you do so, if anything, it will give you peace of mind. If the nodules are growing and the ENT wants to remove them, I would listen to him. I had my thyroid removed in October due to 2 nodules and Hashimoto's disease and do not regret it. The battle is to get the thyroid meds at a proper level, but for me I was already feeling terrible and so the adjustment is already an improvemnt. If you choose to leave the nodule in be prepared to be monitored and frequent biopsies to make sure that the nodule does not actually become cancer.
Good luck you in your search for a strong and healthy body and remember the most important thing to remember is that you need to trust the physician that you go to if you don't keep looking until you do.
Agree with 898_1. My biopsy missed my cancer, it read "benign follicular clusters", which meant no cancer cells, but the clustering concerned them. Even without cancer, it may be pressing on your windpipe or Laryngeal Nerve, that controls your vocal chords. The bigger it gets, the harder it is to remove it without damaging the nerve and preserving the parathyroid. The surgery is pretty simple, not too bad, I had it twice. Barely a scar, no complications. Get it out and get it tested. It won't go away and will only grow.
Unless nodule is simple cyst, most rapidly grown nodules should be removed as biopsy of the large nodule can miss the cancer cells. However, before proceeding, obtain a second opinion from thyroidologist