The issue here is whether the tire company was negligent when they put your new tires on the car.  If both the police and the two truck driver provided statements/reports stating that the tires were not put on your car properly, this would tend to suggest (from an evidentiary perspective) that the tire company may have been negligent.  If you can establish negligence, the next issue will be what kind of damages you can recover.  Although you do not go into detail with respect to your injuries, obviously you could potentially recover for any injuries to yourself or your property that you received as result of the tire company's negligence.  Another issue that may concern you is whether you may be liable for injuries suffered by the other driver, which is another reason it will be important for you to establish that the negligent party was the tire company, not you.  For all of these reasons, I suggest you consult with and/or retain an experienced personal injury attorney at your earliest convenience in the interest of protecting your rights following this accident.