Car crashed due to someone running a red light
Recently, while I was crossing an intersection with a green light, someone who was stopped at a red light suddenly started driving towards me, as if aiming to ram into me. I wanted to avoid the T-bone so swerved right as soon as I noticed it, but then crashed into a tree on the intersection sideway. Police came and reported the other party as witness only, as they had no physical contact with me. My wife and I had to go to the emergency care. The car is totalled, but I'm yet to hear back from the insurance.
My question is, can I sue the other party for negligent driving? Should I sue them before or after claims are settled? Or do I let the insurance handle this? I already provided my insurance with dashcam footage.