Hi Suujoy,
It can be very hard to find folks that really know what to do in this situation. It is even harder to know how long to be patient. While I was in ICU I saw a specialist several times, had a barium test, and given the advice to turn my head over my shoulder to eat and drink. Some winks after leaving, I had a few sessions with a speech therapist who really wanted to be cautious about the types of exercises to give me. Over that first year, I had three larynogplasties (injections) of the paralyzed vocal cord to plump it up and move it more to the center. While these helped, they never lasted as long as they generally should have and so my voice was very soft and strained. Just before seeing the ENT handling my vocal cord issues to schedule the same sort of surgery that Susan mentioned, i noticed significant changes that were very brief, but very real. We decided to forego the surgery and let the recovery continue unharrassed. It seems to have been the right decision for me. I still have limits, but in most indoor situations the normies can't tell.
If the nerve was not damaged only stressed/strained, I would think you would have good hope of eventual recovery. The key of course the word "eventual" and what you should/should not do during this time. Hopefully you will find a doc or therapist that has a good amount of experience in such things.
For months I was very particular about my diet. I really avoided things with crumbs or that were very dry. Breads, cookies, even pork and steak, I avoided or saturated and ate in very small bites. Even now I tend to avoid things with small particles or are very dry as they still irritate both the vocal cord and my throat (I still have impaired autonomic swallowing). However, once I got used to what I needed to do, it wasn't so bad. In fact, it was an overall improvement in my life to be intentional and thoughtful about my eating.
I wish you well. Life is good and I wish all my friends to be able to enjoy it the way I do.
-Tod