Lane change accident

What is the name of your state? New Jersey
I had a side to side collison right in front of the exit of a freeway. I was on the left lane and the other car was on the right lane. It's a minor accident and we both had a dent on the doors. We called the police and he thought I attempted to exit the freeway and struck to the other car. I got a 'improper lane changed' ticket as a result of the accident.

I want to fight the ticket. Do you think I have chance to win? What are insurance companies most likely to say about who's at fault? Thanks

In which lane of traffic did the collision occur?

On the police report, it happened on the left lane, but I wasn't sure