PTSD, also known as post traumatic stress disorder, does not make you paranoid. But I know what you mean when you ask this question. If you have PTSD, you have been through such severe trauma, that your brain is changed and you spend much of your time scanning the environment for any signs of impending danger, so that you don’t have to endure that same trauma again. After the trauma, your brain and body are constantly in a state of alert and you are continuously on guard for anything dangerous whatsoever- you are in a constant fight or flight response, the adrenaline response to fear and anxiety. So a loud noise or sudden movements may startle you and make you jumpy. You also avoid any reminders of the trauma, and when confronted with such reminders, you make every effort to leave no matter what.
No wonder people may think you are paranoid. Paranoia is another term for paranoid delusions, where you have a fixed, false belief that someone is trying to harm you. This is different from the hypervigilance and being on-guard that comes with PTSD, as you are trying to anticipate and scan the environment for any danger, as you do not want the trauma to occur again. If you have PTSD, you may believe that people are trying to harm you, but this would only occur when you are re-experiencing the trauma in which you were actually being harmed- so you only believe this when you are having a flashback or a nightmare of the trauma. People with psychosis and paranoid delusions believe that people are going to harm them and they do not have to experience a flashback or nightmare to have paranoia.