Now as a lifelong loner (relationships in a Pakistani household do not mix) I see the main problem.
Your relationship was long distance: this requires trust, a lot of it. And like the absolute melon you are- you broke it. Now you want her back as you love her, but she doesn’t want you back from what it seems.
Personally I wouldn’t want to continue a relationship with an unfaithful person. If she’s moved on you will have to come to terms with that and will learn.
Apologise to her if you haven’t already, and don’t expect her to continue the relationship.
But blunt but I’ve seen how cheating tears apart families; things will not be the same.