It happened at an apartment in the 200 block of North Lumber Street Monday.
Police said the teenager and 53-year-old Joseph Williams both died on the way to the hospital. Williams had a single gunshot wound and died from injuries suffered in the fire.
The medical examiner in Raleigh conducted an autopsy on the son Tuesday. It was determined that he died from injuries sustained in the fire and multiple gunshot wounds.
An autopsy is scheduled for Williams in Greenville on Wednesday.
The Nashville Police department and the Nash County Sheriff's Office are investigating .