Can I be charged with a DWI for a hit and run?

I'm wondering if I can still get charged with DWI after the night. I was not pulled over, I did no tests of any sort. Only thing I did was a hit and run. Apparently I swerved into another vehicle and they got my license plate and reported it. I only found out because I went to a voluntary interview and spilled the beans that I had been drinking. At the end he said I was gonna be charged with a hit and run charge for sure, but I want to know if they can still pursue a DWI case against me.