Was it the psychologist who told you the diagnosis is PTSD? To be confident in the dx, I would prefer the diagnostician to be a psychiatrist. This doctor has equivocated, saying you can answer "yes" or "no". Given that, it would appear that this person does not see your mental illness, to the extent that one exists, to be "serious". I remain of the view that, given what you have related so far, you could not be faulted for answering "no", you do not have and have not had a "serious" mental illness. Sure, you could answer "yes" and go on to explain, but in your shoes, I would eschew that approach. It will might lead to a whole new line of inquiry that will not likely be of benefit to you. But, of course, entirely your call.
In the end, I suppose we can say that, in your situation, there is no answer that is the only possible answer to the question. In my assessment, you would be on safe ground and your position entirely defensible were you to answer "no". If your comfort level tells you to answer every question in the manner least favourable to your position, thinking that doing so makes you appear scrupulously honest, then by all means, act accordingly.