Just fyi, where I got that from.
https://www.sosuave.net/forum/threads/banged-2-girls-in-her-bed-am-i-ok.253738/page-2
I would advise to think more with your head on this, rather than your heart. I don't think you guys have any level of trust with each other, which as corny as it sounds, really is the basis of building any relationship. After you've guys decided that 'We're gonna give it a go' (stating that you're essentially cutting off other girls, focusing on her (
link)), something in you decided to go out and pick up two different girls to bang (and also lie to her about it, when she can 99% tell it's a bull**** lie). Probably because things weren't either what you pictured, it was going too slow for you. Maybe it was simply boring. But people aren't dumb - you bring someone in your room for the night, it's near damn 100% you're banging. Or extremely close in any regard. So obviously this is going to piss her off (and remove trust, get her to back away, etc.).
Your need to be loved and wanted is a natural feeling (being a social creature), but you need to culture that ability to get it from yourself. It's a difficult thing, but you can definitely get some fraction of it, enough to prevent this back and forth movement of 'head and heart'.
I'll opinion it like this: this relationship is ****ed. It will not work out. The drama upon when she moved in was the first sign of this. And I don't think you really want to be committed to her (which is fine). I think even if she gave you all the sex you wanted and more, you'd still be out picking up chicks for the fun of it eventually.
Keep looking, and eventually you'll find your match.