My question involves a traffic ticket from the state of: WA

Hello, I was involving a car accident. In an intersection a car in front of me wanna make a left turn in a green light, so I slowed down and try to change a lane. But I didn't thoroughly check the right line and there is a car in my blind spot side sweep me and smashed me to the left, so i hit the car in front of me as well.
The police came in and I was too nervous that time (my first traffic ticket). I told the police I have to change the lane in order to avoid hitting the car in front of me. The police issued me a speeding ticket with code 46.61.400, Speed too fast for conditions. But after I came home and watched my dashcam, I realized that my speed was actually only 13 mph on a 35 mph road. I hit the other cars because I didn't check the blind spot or the car driving behind me was too fast. It's also rainy and dark that day (you know the Seattle's rainy season).

So what should I do? Since this's my first ticket, should I simply ask for deferral? Or how much possibility to win if I contest? The problem is I don't think I should receive the speeding ticket. But if the judge determines I was actually driving carelessly, is that sound more than like a "neg-2" infraction which is more serious?