Possible thyroid enlargement I think. Dr says no. What now?

Thyroid. Its called goiter. Ask for a thyroid ultrasound. Minimally ask for an antibody test that can detect inflammatory agents causing the enlargement. Thyroid function test as well. If you've got a family history of thyroid disease in first-degree relative, you should be screened anyway.
Get 2nd opinion. Have another doctor give you second opinion. I would suggest an endocrinologist or a surgeon with thyroid experience or an ENT (ear, nose, and throat) doctor.