This is bad. Even if you "get off" you really need a lawyer for something as serious as reckless. So even at that you have lost money.
Sounds like either you or the other guy (lied?) and the cop concluded you did something wrong. This amounts to your word against the guy who hit you. Too bad you don't have witnesses.
But the weird thing, is, most of the time a rear end deal is the guy's fault who is in the rear. "No matter what you are doing" someone following is supposed to allow enough time to stop. Maybe he claimed you suddenly swapped lanes.
I know it's too late, but investigate Chinese imported "dash cams" "for next time." You can get them with front and rear cameras, I got one for about 80 bucks.
I would supena / request the cop's and the other guy's statements. I hope YOU did not "blab" too much. This idea that cops are "trying to help you out" is bullshit.