Honestly, I would go and file another restraining order. They will give you a temporary restraining order, you might get denied a permanent one but that is another day another issue. This is about your safety in this moment, today.
The other issue that although a restraining order is nice to have, it is really only a piece of paper in the end. Is there anyone you can stay with? Anyway to go somewhere where he won't know your where abouts? It sounds like your neighbor told you for a reason, that he knew it wasn't a joke and that he was actually worried for you safety. The fact that you would be hugging and kissing and he would say "If you leave me i'll kill you" makes me have goose bumps since it comes across as a warning.
I'm sorry you're going through this, do what YOU need to do to keep YOU safe.