Will I be tied to a hit and run?

I was driving a car Friday night that is not registered to me with out of state plates, and I hit another car. That driver left, and I left the car behind because it wasn't drive-able. I left the scene because I had been drinking and was afraid of a DUI. There are things inside the vehicle that have my information; one being some business cards inside a portfolio I left behind. Will the police use this to say I was involved and charge me? Even worse, will they show up to my office to question me? What should I do and can I try to 'prove' I wasn't the driver? Side note; the owner of the car is a family member and is aware. They called to find out details regarding the pick up of the car, and was told it is being investigated for a hit and run.