Cheated on girlfriend of 5 months. Should I tell her?

Some background:
I met my girlfriend at a party 2 years ago. We hooked up the first night and started hanging out literally everyday after that. I knew she was sleeping around with other people, and so was I because we weren't together. But I really liked her but she did not want a relationship at the time. About 4 months after being more than friends I found out she hooked up with 2 other guys in my house while she and I were also hooking up (the first a week after we hooked up and the second about a month after we started to hook up). She lied to me about the entire time until I found out through a friend. It broke my heart. Devastated me that she would go behind my back and hookup with people I am friends with. It also hurt my friendship with the 2 guys she slept with. And worst of all, after both those nights, she crawled back into bed with me because I went to bed early while she stayed up and hung out with the guys. I got my belongings back from her and completely ended things with her and we stopped talking. About 2 months later she texted me apologizing and wanted to remain friends because she thought I was something special. We started to hangout about 10 months ago. We spent almost every day together, weather it was studying together, going out, watching tv. She and I would sleep together 6/7 nights. After about 4 months of hanging out like this, she told me she loved me and I told her I loved her back. About a month later I asked her to be my girlfriend. She is the first girlfriend I have ever had. I am head over heels in love with her. We started to spend around 16 hours a day with her (thats including sleeping). She is everything to me. I can't imagine my life without her. I have not been the best boyfriend tho since I still get very disturbed she hooked up with 2 of my friends. I know it shouldn't bother me because we were dating at the time, but she also did lie to me repeatedly about it because she 'didn't want to lose me.'" So here's what happened:
Two nights ago I cheated on my girlfriend of 5 months with one of her good friends in her sorority. We were drunk at a party (I know this is no excuse and I do not blame alcohol for my stupid decision but I am just giving context to the story) I made out with her and also fingered her. She did not touch any parts of my genitals. She also ended up sleeping in my bed but we were fully clothed. In the morning I was in a world of guilt and regret. The friend says she won't tell anyone because she doesn't want to lose that friendship, but it's eating me alive. I have told her multiple times that I don't lie to her, and until this, I haven't told a lie to her. She trusts me. I have no feelings or any intention of hooking up with the friend again or any girl for that matter. This guilt is the worst thing I have ever experienced before. I haven't eaten, dranken water, brush my teeth, and only left my room to go to the bathroom. I can't even imagine how she would feel if I told her this. I made a mistake one night and I will regret it for the rest of my life. I can't imagine being in a world without her. I have vowed to be a better boyfriend and to try to make her happy for the rest of our time together. I have promised myself to never bring up the fact she slept with my 2 friends because it pisses her off every time I do. I never want to feel this guilt again and I know I will be loyal to her and change to make things work.
The reason I cheated on her is because she slept with my 2 friends and it felt like I was cheated on. I went into deep depression when I found that out. I wanted to get back at her but now I feel like the biggest scum bag in the world. She has made me so happy and I cherish every moment I spend with her. I rearrange my entire schedule for the chance to hang out with her if only for a few minutes. I know what I did was wrong but I don't know what I should do? Should I tell her? If I tell her it would break her heart and will end out relationship (I don't know if we'd still even be friends afterwards), but if I don't tell her, it would be my first lie and a monumental lie. I feel awful for cheating.

Any advice would be very helpful.