One of the agents said that Doug Timmons used armor piercing rounds in his gun. However there are no armor piercing rounds for handguns, they are only made for rifles. It is possible for someone to custom make armor piercing rounds for a pistol, but they would not be very practical as most pistol cartridges do not have the power needed to penetrate body armor, including the .45 Auto Doug has.
LaCroix says that Doug is suffering from PTSS, Post Traumatic Stress Syndrome, because of what he went through during the school shooting when he was a kid. However PTSS is something a person experiences immediately after a traumatic event, it usually resolves within a few weeks. Long term effects from trauma are PTSD, Post Traumatic Stress Disorder, which are often confused with one another. However LaCroix is an experienced FBI agent who was married to an Army veteran and works with veterans, he would know the difference.