Male, 23, and female, 23 - what’s the best way to approach this situation?

I received a message from a girl I’ve known for ten years asking if I wanted to hang out. I responded with a "maybe," but eventually decided against it because I didn’t want to risk cheating on my girlfriend of six years. This made the girl really angry, and out of spite, she shared all our messages with my ex in an attempt to make her leave me. Unfortunately, it worked. The fact that I even entertained the conversation has upset both my girlfriend and me. Now, my girlfriend has said she’s not ready to see or talk to me yet, but she’ll reach out when she is. We haven’t spoken in almost a week. I sent her an email taking responsibility for my actions and conveying everything that needed to be said. This situation has made me realize I have a lot of personal issues to address, so I’ve decided to start therapy to reflect on our relationship and improve myself as a person and as a man. I’m worried she might not give me another chance, but since she’s also my best friend, I want to grow not just for myself but for her. I understand I may have upset her over small things in the past. So, what should I do next? Is there still a chance to win her back? I genuinely want to show her the changes I’m making and how I’m improving.