A person should never be his or her partner's therapist. In your relationship with this wounded person--and I agree, she is wounded--you took on a savior role which just cannot work. There are so many reasons why. Too many to list here. But this kind of savior-victim dynamic in a relationship is not healthy for either person and it is ultimately destructive to the relationship.
The issue, from my reading of your story, is her mental health and her critical need for professional help, for recovery from child abuse, for alcohol abuse or possibly addiction, for trauma. You are NOT qualified to give her what she needs.
She needs a long and sustained amount of therapy. She needs treatment for her disorders. She is unable to meet another human being--you--in a genuine way, and in fact she is so lost to herself that, to add to all her other problems, she would likely become extremely dependent on you for security, self-esteem, and even for her sense of identity.
I write all this with great compassion, for some of my dearest friends come from horrific family abuse, and of those friends, two were unfaithful to their partners. They were messed up by their abusive backgrounds and they had no center. Infidelity does not always mean absence of morality. Sometimes it means a hollowed out shell of a person acting out in self-destructive ways.
But even as I know this, I also know that I personally, once betrayed, could not stay. However, there are others who can work through such a situation and who can rebuild. Every person is different and has different capacities.
The risk in your situation is that you will accept her apology and remorse, repress your anger, take her back, expect her to be a good partner to you, and all without her ever having any therapy or recovery whatsoever. And that will be a disaster. It will also be selfish.
Advise her to seek serious help. Step away long enough for her to really begin to heal (the minimum amount of time is a year, in most cases, and in my experience, it is about two to three years).
Some men like wounded women because they like playing a "father" role to them and they like being the one who is more in "control." Take some time to examine yourself and find out whether you were headed in that direction.
You are both young, under 30, and no one can expect you to have a lot of answers. You have so little life experience. But I tell you, the young woman you love needs therapy more than she needs romance. More than she needs you.