Will I get points from my “careless driving” ticket?

Ok so last night or tonight, I don't even know at this point since it’s so late. l was driving down a large road in New Jersey, and I went to look at my remaining fuel which I can only see by looking over my horn area and down towards the bottom of my dash, anyway I did not see the light had turned red in front of me and I slammed on my brakes to not blow through it, l went over the white line and a bit into the intersection, I then proceeded to put my ass in reverse and back up, luckily no cars were driving through the intersection but unfortunately there was a cop at the light, I got pulled over and got a "careless driving ticket" 86$ and 2 points on my license. I am from New York and my car is registered there, I was just visiting a friend in Jersey, my friend said that he thinks that I won't get the points on my license since it happened out of my state, I don't care about the 86$, I could always just work more hours this week, but the 2 points are what really upset me as I've had a completely clean record otherwise, will I get these points on my license?

Is it worth making a court date?