Most lawyers will say no to represent you if you were at least partially responsible for the automobile accident.
Now, having said that, if your injuries were major, meaning loss of leg, a hand, a huge clearly demonstrated herniated disc injury, some lawyers would take your case. You need to realize that if you were partially at fault even with the injuries I suggested, the insurance company will deny all responsibility. This forces your case into litigation and most likely a jury trial to determine who was at fault.
In these type of cases you will need to have a serious investigation of the facts surrounding the at fault issue right up front. All possible witnesses need to be contacted. A conversation with the police office will be necessary. Without a reasonably favorable outcome from this investigation, you will have difficulty winning your case no matter how injured you are.