This is a long story. I’m a freshman in college and have been dating this girl for 6 months. We have told each other we that were in love and want a future together. There’s just one thing I can’t get over.
Before we were officially dating, we kind of a had a “thing” going. We went to each other’s fraternity/ sorority formals and what not and had sex. However; at a party, I was helping a friend who happened to be a girl, who was very intoxicated. Someone seeing me sit down with her on a couch assumed I was “hooking” up with her. I was not. This person told my now girlfriend this, and she ended up leaving with another guy and having sex with him.
I know this might seem like it was a misunderstanding but it hurt me more than anything I’ve ever experienced. She apologized the next day and I gave myself days to think it over. I decided to give her another chance and we began what is now our 6 month relationship. I am happy being with her, but when I think about this night, it brings back a lot of pain for me, and I just haven’t fully gotten over it. Should I still be in this relationship?
LemonVibe 
No and I was on your side until you said “Before we were officially dating.”
Neither of you are ready for any kind of relationship until you both mature more. You both should date more. You weren’t even dating yet, just checking each other for compatibility, so that doesn’t count as cheating. You need to discuss this with her, but if I were her I would consider this a huge red flag and move on from you. In the real world you can’t hold something that happened before you were dating against your present amore and expect them to stay with you.
“Hey remember that thing that happened two weeks before I told you that I would like to date you? No? Well I am mad at you for it.” She has a right to date and have sex with other people than you if you’re not in a relationship. That is not cheating.
The fact that you are asking strangers on the internet shows that a. you haven’t discussed it enough or at all, b. you know that you are in the wrong and was hoping that someone would say “oh man gawd, she’s a terrible person and you should dump her,” c. that you can’t be trusted with intimate details of a personal relationship.
I do wish you the best and good luck on the dating scene.