You’re on the verge of deciding between two conflicting positions, and it sounds like you know that. If you forgive, you have to make a commitment with your partner to rebuild trust, and if you feel as though the trust is completely gone, there is no way to forgive and you would have to, then, move on from the relationship.
I’m a realist: if the trust is gone for you, it’s gone and if you’ve committed to that realization there’s not much else I can say, other than I think that loss of trust is valid reason to end a relationship, because it’s not fair to either of you.
On the other hand, if things feel a little bit more gray for you than that, and you’re having a hard time thinking about what to do, consider how your girlfriend is handling this. Has she been understanding of your need to discuss what has happened? Has she accepted, and owned up to the fact that she has done something that violated the standards the two of you have set forth in your relationship? Has she helped with any sort of process to figure out how to move the relationship forward from here? Consider this as you try to pull more toward one choice or another.
Of course, I feel compelled to say that, in any rough situation, yelling gets you nowhere. It’s critical for the two of you to have a mature conversation about what has happened in order for you to have closure either way (closure of the relationship, or closure to move on from the situation in the relationship). It will be painful, but it will be worth it, no matter what you decide.