There are two things to consider here, the first being the recruitment process which is very comprehensive and includes mental health as well as physical examinations. It can be the case that for some illnesses the applicant has to demonstrate being symptom free for an extended period of time, others are felt not to be suitable.
It realy is not possible to gloss things over and simply say one has always been free of mental health issues, the examination process brings them out anyway, and if you had got though then you would be in trouble later on for a false statement.
This is not stigma but a realistic appraisal of the conditions under which you might have to serve. These have extreme stress and many who enter the armed forces end up discharged due to severe mental health conditions brought on by their duties.
Given the experiences you have had to face in your life up until now I do not think if I was in your position I'd seek out such a highly stressful lifestyle.
I used to feel I wanted to take my life and tried to do so, it is a terrible way to be, and I now avoid situations that might bring me back to that state again.
I know what it is like to want a particular career (I was a policeman) and not being able to start (or continue on) in it. It can be a great disappointment and I'm sorry my reply is so negative.
Do you have a second choice apart from the military or similar high stress dangerous careers?