What should be done if I got a DUI, but I was not driving the car?

I came out from a local restaurant after some social drinking. After leaving the establishment, there had happen to be an ambulance waiting for a call. I was feeling very sick and had asked them to check my blood pressure and a ride to the local hospital. I'm guessing the ambulance EMT notified the police which in case lead to the DUI. However, the car was parked. I did not enter the car nor intended to drive home. I was outside the car entire time in the parking lot. Therefore, I never drove the car. In my opinion instead, I should have received a public intoxication and not a DUI since I never drove the car or had the intent.