Is my neighbour being threatening towards me?

Sounds like you're afraid that he is going to physically attack you, but don't worry I doubt he'll go that far. People harass each other all the time but it's rare that they attack, especially when the argument is with a girl since most non-third world country cultures are against hitting women. I suggest you try to resolve it instead of "talking back" to him so to speak because that will just make it worse. I'm only assuming of course, I apologize if I was wrong.