Yes, acid reflux seems more appropriate...you can test this yourself before seeing a doctor by going to the drug store and getting Prilosec OTC, take one pill 1/2 hour before breakfast and dinner for two weeks, and see if it helps. If the coughing gets better, you probably have gerd.
Thyroid cancer can potentially cause hoarseness or difficulty in speaking in a normal voice, trouble swallowing or breathing, pain in neck/throat and swollen glands. On the website I looked at, they didn't list coughing. However, coughing can be a sign of acid reflux disease- so you may want to consult a gastrointestinal specialist if you suspect that might be a problem for you.