Having something wrong with your brain/genome/body can cause you to be violent. And will probably not be considered psychiatric in etiology (as witness it is not listed in the DSMIV).
You're mixing up different systems of classification. I think you may be mixing up the terms functional and psychiatric.
The different terms are used as layers to try to understand the aetiology.
The first layer is very broad. Essentially organic versus functional illness, organic meaning caused by a problem with the body, functional meaning not caused by an identifiable problem with the body. Bad behaviour, factitious disorder, conversion disorder would all likely fall into functional. The major mental illness such as psychosis fall into organic.
The second layer is a little more precise. An organic illness may be structural, infectious....etc in origin.
Then a condition may be congenital or acquired.
Schizophrenia is a condition that is organic, related to neurotransmitters in the brain, and can be congenital or acquired.
Heart wall defects are organic, related to a structural problem in development, and congenital.
The fact that something is organic and congenital in no way excludes it from being a mental illness.
"Psychiatric" is a very poorly defined term that may be precise in naming some conditions such as depression, may mean "listed in DSM or ICD", or may be nothing more than a social judgement. Survey enough people in the street and they'll tell you that people with violent behavioural problems, alcoholism and even deviant sexual behaviour need to see a psychiatrist and "must have some sort of mental illness". Ask them a few decades ago and being gay would have been included on the list.
I totally agree that assuming a behavioural problem is "psychiatric" is something that society will probably be ashamed of in a few decades time like we're ashamed of the history of locking up single mothers and homosexuals now. These inclusions based on society's judgement are things that greatly add to the stigma of having a mental illness.
My advice to the OP is in two simple parts.
1. There is no illness of any organ or system I can name that presents with unprovoked rage in more or less clear consciousness that is followed by complete memory loss. The clear consciousness part is the bit that takes epilepsy into account as seizure activity typically happens in an altered state of consciousness and is typically semi purposeful. Someone in the midst of a seizure may trash their room, or hit someone for example, but no-one has ever tidied up their room or done someone a favour during a seizure. Seizure activity typically leads to very simple, instinctive behaviour.
2. If the OP subverts an existing "mental illness" label to make it match the factors they need to progress their story ,then they risk adding to the stigma of having a mental illness by propagating the idea that people with a mental illness may be dangerous in ways that they're typically not.
Craig