Friends Breakup

Manuela
Ok so I fell really heart broken, my best friend Anna doesn't want to be involved with me anymore for a thing that I didn't do. I was partying with some friends and her ex bf Jack was trying to get with me and of course I did not want to do anything with him. 
I was a little drunk so I went to my house with some friends and one of my friends invited jack and he was drunk, I went to smoke with some friends and then I went to my bed to sleep. The next thing I know when i wake up is that the guy sleept in my couch with my roommate's permission.  
So people started talking and now Anna thinks a had something with Jack
 I talked to her and she doesn't want to be my friend anymore. It hurts so bad to loose a friend. I loved her like a sister and now I just feel pain, like a breakup pain.
 Should I fight to win her friendship back?
How can I do that? 
Is it worthy?