moving violation

I got a traffic ticket recently in NC state and here is what had happened.

My car was parking in a parking lot near a store. When I walked out of the store to my car, everything was OK. I went into the car, looked back, it was clear. I then started to back my car. And I did keep looking back as I continued backing my car very slowly. It was still OK.

Suddenly, I saw a car on my left side, and before I was able to do anything, these two cars bumped together. That car was in the driveway, and it was perpendicular to my car. And that car's rear bump was in contact with the left side of my car. So, I drove forward Returning to my parking place.
A policeman came, and the driver of the other car said he was stopped at that moment and I bumped into his car. I thought his car may also be backing because, if not, how come I did not see that car earlier and only the left side of my car was in contact with the back of that car?

Anyway, the policeman gave me a ticket saying "failing to see before backing from a direct line that such movement could be made in safety"

I need help because I used PJC to waive another 4 points 6 month ago. I am afraid that if I don’t fight this ticket, those 4 points may be accumulated back to my record.

So, my questions are:
1) Should I appeal for non-guilty or guilty? If I agree I am guilty, is it possible that my points for this time be removed? If I appeal for non-guilty but failed, is it possible that my points for this time still be removed?

2) If I can get the points for this time removed but still pay the fine, will the four points of last time be reversed?

Thank you,