Yes, EMTs (emergency medical technicians) can get PTSD (post traumatic stress disorder). EMTs develop PTSD from vicarious trauma, where they experience and witness the effects of traumatic events via the patients that they treat. Seeing the devastation, deaths, and trauma injuries can induce PTSD in EMTs, even if they did not experience the traumatic events directly. So EMTs can develop PTSD from indirect exposure to the trauma- seeing the aftermath of the traumatic event is enough to induce PTSD.
