Max,
My first surgeon explained to me there is a small facial nerve that could be caught and would cause the right side of my mouth to drop. He wanted to warn me because he was pretty certain it would get cut or nicked during surgery. He summed it up by telling me to take a look at Sylvester Stallone as he had it severed with forceps at birth. Well it got caught but I don't believe it causes the numbness I get.
I am almost six years out from treatment and I seem to get real numb in my face and neck when I don't stay hydrated. I wasn't told of a nerve in the neck that you mention but wouldn't discount that. I have a spot under my right cheek bone that stays numb but it's just above the scar line so I figure it's from the scar tissue inside my mouth.
I have neuropathy due to chemo but doesn't seem to be in the face/neck area, it's more in feet, arms and hands. Do your best to stay hydrated and possibly this will help. Best wishes to you.

Steve