Everything Done Correct

It was a sunny day and I was transporting a patient emergently from one facility to another. The patient was a minor, so the patient was being accompanied by a parent who was riding up front of the ambulance. The patient was being cared for by a paramedic. I was driving as a newer EMT in a larger ambulance. The ambulance was a Chevy C4500 Kodiak with a full size box. I was coming to an intersection where there is a right turning lane, two straight lanes, and a left turning lane. Where we were at, there is a lot of traffic. The light I was coming to was red. All of the lanes, except the left turning lane, was full of cars. I turned on my turn signal to indicate I was going from the left straight lane, to the left turning lane. At the intersection, I needed to turn back in front of the other three lanes of traffic to make a right turn. Once I was in the left turning lane, I turned my right turn signal on to indicate I was making a right turn. I came to the instersection where it was still red. I proceeded through the intersection beginning to turn infront of the left straight lane. While making the turn, I noticed that the light had turned green for the straight through traffic I was turning in front of. I looked out the passenger side mirror and noticed a passenger care start moving towards me. I attempted to steer away from the vehicle, but was struck in the back rear passenger side of the box. After doing everything that was appropriate, I still managed to be involved in an accident. I am glad it was low speed, but anything is possible.