Hi..
I'm a vocal instructor, and I would like to express to you how sorry I am that you're experiencing this difficulty.
With paralysis of the vocal cord, what I would suggest is that you find a good otolaryngologist (ENT)who can then refer you to a speech therapist. There are sometimes surgical solutions to loss of cord use, and then sometimes, therapy is recommended. You want to find an ENT that specializes with singers. This way, you're sure to find someone that concentrates on the voice. You can find this person by doing a little investigating. Call a University or college in your area, or maybe a local theatre/performance group and ask to speak with the choir director, or stage director. This person will likely have the name of a good doc in your area that can help. Actors/singers always need good doctors, and their doctors will likely be people who specialize in the vocal mechanism. Good luck, and I hope the best for you.