I'm sorry you're going through this. My BF and I had the exact same falling out. I got engaged, she was jealous, got drunk and proceeded to tell me how unhappy she was with her life and that she couldn't stand to be around me because I was so happy. I was so hurt that when she called me the next day to apologize I couldn't get past it. We had been BF's since elementary school and didn't talk for the next 5 years. She sent me emails, called me and even sent a letter. All easy for me to ignore. I was happily married, had a beautiful daughter and wasn't interested in revisiting a part of my life that had turned so bad.
One day, there was a knock at my door. My ex BF was standing at my door holding a bouquet of flowers. I opened the door and she broke down crying telling me how sorry she was and how much she missed me.
Well I couldn't help it and I started crying and we immediately hugged! We have ben BF's (again) ever since.
I guess what I'm saying that when I received her emails, letters, phone calls I couldn't feel her sincerity so I ignored them. It wasn't until I saw her face that I knew she really did "mean" it. That's just my personality though. For others an email does help!
Just another suggestion, maybe you can go see your friend. Stop by and tell her in person how sorry you are about what you said 7 years ago.
I wish you so much luck that whatever you do to try and make amends, that you prevail! Let us all know what happens!