Not really, there are semi-auto hand guns (Glocks for instance) that have the “safety mechanism” built into the trigger. By initially squeezing the trigger the safety is released, further squeezing of the trigger, the gun will fire. If the woman had her finger on the trigger when the car swerved or collided with another, her reaction could have been to tighten her grip on the weapon to keep from dropping it, thus accidentally firing it, thus shooting herself. Speculation on my part? Perhaps but I can see this happening.
It is just very unlikely and there is no explanation as to why the guy swerved and hit the other vehicle.