driving rental purchased by someone else , got hit from behind while stopped at red light , what to do ?

The fact that you were driving a rental car does not have any legal effect of any type on your ability to pursue a claim. If you were injured, then you need to seek immediate and prompt medical attention.  Take pictures of the property damage. Hopefully the police were called and an accident report completed.  If so, then by now you have been swamped by phone calls and letters offering legal and medical services.  Be careful with whom you speak. If you are in SW Ohio, then we could assist you.