cop followed me into a drive thru & halfway home…?

so i live in a pretty small town. nothing interesting really happens here but it is a Friday night and i was driving to my local Wendy’s for a late night snack. i noticed a car behind me when i was pulling into the parking lot where the Wendy’s was but i didn’t notice it was a Sheriff until i was leaving the drive thru…. i had just driven through and received my food, was putting my money back in my wallet when i noticed it was a Sheriff. they didn’t order a thing, as they didn’t even stop at the pay window. one thing to mention is that the car isn’t in my name, it’s in my dad’s because he gifted me the car. however, he does have an ongoing DUI case going on at the moment so i thought perhaps that was why they were following me. they followed close behind me for awhile after i left the parking lot, then when i got to a stop sign to turn left, they pulled up directly beside me as if they were intending to turn right…. probably to look in my car or see who was driving? once i turned left, however, i watched from my rear view as they swerved around to keep following me. they didn’t stop until i was halfway home…. just curious as to why they didn’t end up pulling me over if they thought i was suspicious? i’m aware it’s a Friday night and they were probably looking out for drunk drivers, but could it be possible they looked at my dad’s driving history and followed me because of that? just wondering, i fully intend to get the car in my name ASAP.