What should i do with my careless driving ticket? new jersey?

long story short my friend got drunk so i was driving his car, me him and his girlfriend where out to eat, when my mom texted me she was having a bad asthma attack and i needed to get home quick with my inhaler, so i tried getting home fast, well my luck got pulled over 75 in a 50, the cop was being a dill but he ended up giving me a careless driving ticket instead of a speeding ticket, from what i know i that cd ticket is 85 dollar fine with 2 points, (this is my first time getting a major ticket with any points) and id really like to stay at 0 points and keep my insurance lower, (just got my basic liscence in november, and never got a ticket on pro. license) im not a wealthy person so does anyone know the fee of going to the court date and pleading not guilty an seeing if i can get no points added on? and what would u do in this situation? please help im mad stressed,,