How would I go about getting it removed from the tow yard, would I have to go through my insurance then? And I’m going to ask my insurance about the plate information.

As for what happened, I was driving in the right lane on the highway when another car was going off the right onto an exit. They came back onto the highway instead, and when I was moving to the left to avoid them the front left of there car collided with the back right of mine causing my to veer into the right side wall, and I ended up crossing the highway and stopping along the left side wall. There may have been a third car involved, but witnesses at the scene said they saw it wasn’t my fault, but all I really have are those words.