Can you sue your insurance company for injuries if you got the ticket for the accident?

I'm hoping you'll re-visit this site and rephrase your question, because I'm not sure what you mean and I'm very curious.

Typically, you would only need to sue your own insurance company if they've breached your policy, or contract, with them. This is called "bad faith." It might occur if, for instance, you were injured, have medical coverage, and your carrier is refusing to pay. Or perhaps you were at-fault for an accident, got sued, and your carrier didn't didn't defend you.

At any rate, I'm still curious as to exactly what you mean...