I recently met a girl through a friend and were hanging out for a about a week and a half. My friend told me that I had a real shot and to go for her and to be serious. I put in a lot of effort but when I asked her to go out on a date she said yes but then told me it was already complicated with another guy. I talked with her the next day and said that I didn't want to be a second option and after talking for about an hour she said that she would choose me. She then texted me the next day and said that "she was thinking alot and was not okay". Her friend then told me that I messed up and that she was going to end it with me. I realize what I did wrong but how can I remediate the situation?

Actually it seems you guys not even started so there is no question of ending anything unless you guys not going to be friend anymore. I think she is honest to admit previous engagement. So I would suggest to accept her descion and stay in connected as good friends. You never know what future has stored for you.

You do nothing. There is nothing to fix. You never dated. She chose to stay where she is. Move on.