She Has to Help You Forgive Her
You want to forgive Tina, but you also have to realize that getting past this issue is not just your responsibility. It's also Tina's.
Whether you were separated when she slept with her exboyfriend truly is not the issue at hand. The issue you have to deal with are your feelings about what she did. How do you feel about it? You have to be able to articulate your feelings and explain them to her.
Also find a way to explain to her how she can help you trust her again and what she can do to help you forgive and forget.
Let her help you forgive her.
Without her help, you will never be able to get past this. You have to be able to be honest about your feelings, and she has to be willing to accept and take the responsibility for her actions.
Tina's comments about her exboyfriend tricking her into feelings ways she didn't...no one else is responsible for your feelings. Tina herself is completely responsible for her feelings. While she can't always control what she feels, she CAN control what she does with them. So whether or not she believes her feelings weren't real, her actions were and she needs to own up to that.
Everyone has the right to choose, and if her right to choose were taken from her, this would be entirely different question. She chose to behave as she did... You need to come to terms with that, as does she.
You're both young
This is such a cliché, and I remember rolling my eyes whenever anyone said this to me at your age, but it's very true...you are both so young and you have your whole lives ahead of you. This is the time that you should be learning about yourself, learning about what you want and who you are.
Whether or not you and Tina are "the one" for each other isn't so much the point as what you learn about yourselves and each other. If you can take a look at what's happened between you, pull from it what you like and don't like, and figure out just that little piece of yourself, then you've taken quite a step for yourself.
What happened to being single?
I see a problem in that Tina said she wanted to be single because she's never been single before. It doesn't sound much like she knows herself well enough to know what she truly wants. She broke up with you to be single, yet never really achieved what being single means. I never truly understood what it meant to "understand myself" until the day I began to...and it had nothing to do with the person I was with.
But once I began to understand who I was and what I wanted out of life, suddenly the people around me began to change...because I changed them. I had changed my focus, changed my mindset...and began to know ME. Until you've both been given that chance, you may always come into the confusion of knowing what you want and what is right.
To forgive and forget...
You can forgive, by working with Tina and working with yourself. Figure out what you need from Tina to feel safe again, and let her know. Talk to her. Give her the chance to help you out. Once you have begun to feel safe with Tina, have begun to build your trust again, then you will be able to forget.