I was in the same situation, I was riding on Bowery St and was merging on to 4 th ave in NYC when i was moving over the guy in the car speed up to cut me off ( I signal I was moving over).
We stopped at the light and like you we exchanged words.
The guy then ran the red light after I went through and the car behind us happened to be a Federal Marshal watching the whole thing. He stopped him dead on the spot!
Issue him a bunch of tickets (Yes, I stopped to make sure he was getting his).
If I mess up when driving or riding , I will take full responsibilty for my actions so should people who drive.
S/F,
CEYA!