It's possible that the problem with your voice is due to infection/inflammation of the nerves to the larynx (voice box).
If the laryngeal nerves are weakened due to injury or infection, you may have weak voice or hoarseness.
See this:
I think you should go back to the physician, and let him know that his recommended treatment, Mucinex, is not helping you. If you don't tell him, he'll never know.
You can say that a friend thought you might be having problems with the nerves to the vocal cords, and can he check that.
If you go in saying that you asked around online, and this is what you think it is, he's likely to react badly.
Here is some other information that you may be interested in.
Serrapeptase is an enzyme that can reduce the inflammation of sinus infections, and thin the mucous. I know of several others on a health board who have tried this with good results.
You can google for Serrapeptase.
Here is one site, with information about research.
If you decide to buy some, look around for a vendor with a good price.
(This is not a prescription item.)
BTW, you asked for a "qualified medical opinion" on a patient to patient forum.
I'm a retired R.N. with some experience in doing patient assessments.
If you'd like the opinion of a physician, you can post on one of the Doctor-to-Patient forums, like the Respiratory Disorders forum, or the Undiagnosed Symptoms forum.
http://www.medhelp.org/forums.htm
Let me know what happens, okay?
Wishing you the best,
Carol