I just want to do the right thing.
The right thing for you to do now, fella, is to get on with your own life and understand that whatever connection you had with this woman is over (or at the very least irreparably damaged) and as such she is not not your problem anymore. I tell you this from painful experience - you cannot help her, you cannot fix her and any further involvement for you in this capacity, plus your emotional connection, will only lead to more pain and difficulty for the both of you. It sounds like she needs professional help. You are not a professional, so don't even go there, even out of your well intentioned feelings towards her.
Separating yourself like this will he hard. Very hard indeed. But it is something you must do for your own sake (hers too for that matter).
Take it from me; you will need to be very disciplined with yourself every day to keep your emotional turmoil from getting the better of you - not having her around muddying the waters of your soul with her manipulations (intentional or not it makes no difference to how it effects you) will mitigate the potential for setbacks.
You will learn something about yourself if you do this.
All of us here understand that sometimes you just need to talk to someone about what's going through your head (even the 'alpha' dudes will admit this), and whilst it is still early days for you, you have to start moving forward and not spend the next several months treading water with your emotional state. Failing to do this will only lead to you loosing what's left of your self respect and you'll end up being a whiny little bitch wallowing in self pity and never doing anything positive to change your circumstances.
You need to take control of your life and your interactions with the people in it instead of simply reacting to how other people behave toward you. The sooner you start to do this the better a man you will be for it.
Sorry if I come across as a cold hearted *******, but women with depression and suicidal tendencies who require you to provide infinite counsel and solutions to their problems should be avoided like the damned plague. A few of the guys I've known have been drawn to these problem women over the years, (they always seem to go for the same types) and the relationships always end in the same way; the guys with the best intentions never able to stabilise their partner until all the promises of a better tomorrow begin to fall on deaf ears and the woman finds another host to leech the happiness out of. In this particular case the irony of it is that the needy, problem filled, safe option ended up shagging someone else.
In the interest of equality I should say that everything said above is true of women who date problem men as well.
I absolutely agree.
Like I said before OP - you need to look after number one until you feel you are comfortable enough in yourself to enter another relationship on a more sustainable and equal footing.