Can I sue for personal injury even though I was cited?

I was in an accident and cited for improper left turn. Both were traveling toward each other and we had the green light. Because there is no turn signal attached to the light, I stopped at the green light because I was about to turn left. As I waited for the oncoming traffic, this one car was further off so I made a left turn. As soon as I got over to the other street she hit me so hard until I flipped over and landed upside down. Also, there were witnesses at the scene.