The weight of your breast pulling on your bra strap is what causes your neck, back and shoulder (trapezius) pain. A breast reduction will greatly reduce all this and maybe covered by your insurance.
Thank you for the question and while I am sad to hear you had a bad experience with a breast reduction, there is no association of thyroid disease with breast surgery. So see an endocrinologist and be worked up for your thyroid problem.Dr. Corbin
Your plastic surgeon is in the best position to review your results and determine your suitability for surgery as they have an overall picture of your medical history and current health status. Generally speaking these issues would not preclude you from surgery.