The best source of information about this is going to be your doctor. The problem is typically not the vocal cord itself. The nerve that works the vocal cords runs through the thyroid, and during thyroidectomies, it can be damaged. That is one of the listed possible adverse side effect issues of surgery . Sometimes, the nerve is —for want of a better word — bruised, and will recover. Sometimes it is more severely impacted. Your doctor is going to be your best guide for assessing what is going on.