Can neck injury from a car accident cause problems later in life if it was not properly rehabilitated?

Maybe. Although its possible it really depends how severe your injury was. It's unlikely a minor sprain or strain would result in significant pain years later, but if you developed a disc herniation with radicular pain, and never had it treated, it might be possible.
Not realy. If it is a significantinjury you will notice symptoms right away& seek help without delay.