When should I go to the doctor after a car accident in Michigan?

As soon as possible.

In addition to insuring your health is a priority, immediate follow up with a doctor will also provide official documentation of your injuries. This evidence will be key to your being fairly compensated for the damages that resulted from the accident. 

Specific to Michigan accident victims is the fact that every injured person has a duty to mitigate their damages when an accident is caused by another person or entity. In other words, if you do not seek proper medical treatment, and it results in the worsening of your injury, then you are not entitled to receive compensation for your worsened condition.