This sounds like the 1999 Frank Robinson novel Waiting. Points that match
I think the novel or long short story was published in the last 10 years.
Partial Match: This was from 1999, so a bit farther back than indicated, but still relatively recent.
It starts with a man who is killed in a car accident. A doctor autopsies him and finds out he is not human, that he is built to live longer than a normal human.
Match: A man dies in the car and effectively rips the steering wheel off. Without too many spoilers, the man that dies in the car accident is not truly 'human'
Before the doctor can make his findings public he is mentally herded by someone into dying in an accident.
Match: A doctor dies under seemingly impossible circumstances just as he is set to deliver a lecture to a circle of old friends....he learns that the doctor had compiled evidence <>.. and was killed to suppress it.
The rest of the book involves a normal human who gets involved somehow. He even finds out he is married to a superhuman.
Match: One member, television producer Arthur Banks, sets out to uncover the killer.