PTSD is often associated with combat military service but there are plenty of people who suffer PTSD from other stressors. Common examples are EMS/first responders and victims of repeated abuse. I think you explain your PTSD be simply telling the ALJ what is going on with you...what your symptoms are, what seems to set them off, what seems to make them better, etc. Hopefully you already have medical evidence supporting your claims so your testimony shouldn't be about the diagnosis and should instead be more about how the condition affects you and most importantly your ability to engage in basic work activities.
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You will have a chance to explain your symptoms. It is important that your complaints are consistent with the medical records and your other reports in the social security file. Your doctor should be providing opinions about your limitations also. Military or not, those are the things that you need to do to help the alj understand your case.
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