The prognosis for this fish could either be very good, or very bad.
I lost several Betta fry to a type of lockjaw problem similar to this, where they had their mouths wide open and could not shut them. They died in a very short time, because they couldn't eat, and, as they were fry, going very long at all without food really wasn't an option for them, and they starved to death. I never really figured out what caused their problem, and I've had no other recurrences since the first few fish.
However, as evidenced by other posts, there are other people who have fish who can't close their mouth all the way, and they do fine.
The key to survival is being able to eat, really. It's possible your little Neon just damaged the muscles of the mouth, and it will heal and be fine. If the little fish can eat, then the outlook isn't all that bad. It'll either heal, or it won't. If the fish can't eat...then it's probably doomed in the long run. Now, it might not feel like eating for the first few days if it's mouth hurts, but, with an adult Neon, that shouldn't really hurt it any.