I think the whole thing about text game on this forum is overblown. Yeah, most guys have a terrible text game, but that's the thing... Most guys have a terrible text game and are still getting laid and getting relationships. A girl who likes you will forgive a lot of stuff. Text game is most important before you meet in order to convince her that she should hangout with you. The only exception is if you're just ungodly cringeworthy and needy to the point of seeming like a creepy stalker--that's a different story, but usually not the case.
My take on this still stands the same... She's recently out of a serious relationship and not over her ex (I mean who likes their ex's pics on Instagram months after they've broken up? Oh right, a person who wasn't ready for the relationship to end and is hanging onto their ex for dear life). She was using OP, and who knows--maybe even other guys too before him, in an attempt to fill the void her ex left. Essentially, she's desperately trying to fill her "ex void" with attention/sex/rebounds, but it doesn't work because she was in LOVE with her ex and no new guy can compete with that love (UNTIL she manages to move on from him/loses those feelings for him). She liked OP enough to not only bang him several times, but also WANT to go out on legit dates with him (and not just bang). If she just liked the sex, she wouldn't have wanted to do anything but bang with no strings. Thing is, she was probably comparing him to her ex the entire time, and when he didn't bring the same feelings out of her that her ex did (LOVE) she broke it off. But like I said, no new guy can compete with that. OP was doomed from the start.
To OP: I know what you're feeling. I've been there. You know what I had to do after my worst breakup? Convince myself that it wasn't over. Convince myself that I WOULD see her again--that everything would be okay with us. Yes, I had to delude myself. Sounds stupid, right? Right. Except this helps you get through the first couple weeks, then you start to talk to other girls, you start to care about the original girl less and less, and eventually you're seeing other women and don't care about her at all or even want to see her anymore. I look back and am GLAD my ex dumped me. I don't even know why I liked her now lol. But you need to be able to function through this first week. It's the worst part. And this was only 3 dates... I'd be surprised if you're not totally over this chick in 2 weeks TOPS.
Oh yeah, and you know what else, OP? This girl will probably eventually hit you up. A few bad tinder (or whatever dating app) dates and a few nights of bad sex and she'll start thinking "woah I fvcked up. OP was lightyears better than these chumps," and come crawling back. There's nothing more sobering than sh!tting on someone and a month later after some failures realizing the person you sh!t on was your best bet.