Good question! I usually recommend my clients go to a doctor immediately after a collision to get checked out when they aren't sure they are injured. Better safe than sorry. You would be surprised how many times they are diagnosed with serious injuries, including one young man who was rushed in for emergency surgery to stabilize his spine after precautionary x-rays at an urgent care clinic. However, if after 3 days you don't think you are injured, and you are experiencing no pain, discomfort, or other symptoms, you most likely are not. If you develop any symptoms, go get checked out immediately.
Yes, you should always get checked out by a doctor as soon as you can. Some injuries do not show up for some days and any pain is a sign of injury. I have had cases where a small pain that would not go away turned out to be a much more serious injury that first thought. Some types of soft tissue injury to the back and neck do not show up for several days to a week or more.