If I'm being charged with a DUI and I wasn't in my car, how does that work?

You stated in your facts that you wrecked your car, left the scene of the accident and while walking  to your girlfriend's parent's house (to call and report the accident), you were approached by several police officers with guns drawn.  You were subsequently arrested for DUI and leaving the scene of an accident.  Your question is, what proof did the police have that it was your car at the time they approached you.  First, if you have not already done so, obtain a copy of the police incident report. The report will give you insight as to why the officers believed you were the driver of the wrecked vehicle.  And of course, if the vehicle is registered to you, and  the cops subsequently find you walking alone, without contradictory information, they will naturally assume that you were driving your vehicle at the time of the accident.  Now, having said that, you may have a defense depending on the time frame and any possibility that you could have consumed alcohol after the accident.  You have not disclosed whether you made any admissions to the police.  So, more details would be needed.  Consult an experienece attorney immediately.