You say you stopped, the officer says you didn't. In the absence of other witnesses, who will be believed?
If you decide to fight it, consult the various other threads here about the process.
An officer cannot deduct points. They can only reduce your charge.
There is no such thing.
It's not exactly common that an officer will pull you over in the exact spot where the offense takes place. They will also use the time to check your plates before they stick their face in your window.
Was this about you not making a complete stop or was this a no right on red intersection?