A little bit of advice for my situation?

Please know I was in a long distance relationship, and i'm trying to see if I can win her back. I made the mistake of sexting another girl on impulse (No photos), and the other girl had messaged my friend talking about me, and she found out I had a girlfriend. So she confronted me about it, and I panicked and told her I didn't have a girlfriend, and that we were taking a "break". I know that's really messed up on my end, but I panicked.. I told her about what happened, and showed her the messages. It was on the 3rd of this month that I sexted that girl, and I told my girlfriend on the 7th since I didn't know how to bring it up to her, or tell the other girl I had a girlfriend, but told my girlfriend when the girl confronted me. She's really upset, and furious with me. It's been about 2 weeks, and she told me she made up her mind on the 16th of this month to leave the relationship. I really do care about her, and don't want to lose her. I've tried writing letters, or write about all the memories we've had together to try and spark her, but she does not seem to want to budge. She also tells me that I lost all of her trust, and that she does not love me in that way anymore, and I understand that, but I want work towards fixing it, and earning it back. I also know what I did was wrong, but this is the first time I've ever done something like this, all I want is a second chance to show her, but she tells me no, and that her mind is set. Is there anyway to try and change that? She also says that she'd much rather prefer someone closer to her that she can see instead of seeing each other every blue moon, but I try to fly out to see her when I can.
A little bit of advice for my situation?
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