Public defender wants to take DUI to trial.

I was charged with DUI & unlawful possession of paraphernalia used to smoke/inject. I was doing DoorDash and my car was on E as I was heading back to the city. My car stopped, as I ran out of gas. I pulled over to the side and decided to flag passersby’s. I was out there for about 3 hours and I finally gave up and went inside the car. I ended up falling asleep, not sure for how long, and a sheriff was at my window knocking asking if I was okay. I woke up & said I was just waiting for someone to take me to a gas station because my car ran out of gas. He asked if I was under the influence I said no. Asked to blow into a breathalyzer, came up 0.000. He asked if he could search the vehicle, and I said yes. Well he found an empty pipe I had in my backpack that i had forgotten about and assumed I was under the influence of narcotics. I got arrested, they drew blood, and results came back positive for meth. PD thinks theres no DUI case against me. This would b DUI#3 if convicted