Yes, a person with PTSD (post traumatic stress disorder) can get disability. PTSD can be quite debilitating, as you may have frequent reminders of the trauma you endured. These reminders come in the form of flashbacks and/or nightmares. As a result of these reminders, you become quite fearful and anxious, which leads to hyperarousal and hypervigilance, where you are easily startled, jumpy, and constantly on-guard for any danger. This can take up most of your time, to the detriment of everything else in your life. Soon, you are not able to function at work and/or school, your relationships suffer, and your self-care suffers. In addition, you avoid any triggers that remind you of the trauma, so you become socially isolative and suspicious.
For more information and help on PTSD, watch the following video: