You both need to talk and it has to be where no matter what she says, you're calm about it and not getting upset.
If you are in a relationship with anyone, one of the most important things is being able to talk openly about anything, and not blowing up and freaking out if she tells you the truth.
I don't think you should be the one going "I can't sleep, I can't eat" to get her attention, it does DLV you a bit. It does come across that you rush things a bit... talking about moving in is pretty serious stuff, and I don't recommend that with someone unless you've been with them for years.
You told her it was over. She told you "we never got back together".
I would probably have a talk with her and find out if she really wants out of the relationship, because it seems that she's keeping something from you. You're both seeing each other once a week, so the reason to break up is because you're both too far is a legit reason and she can't hold that against you. It might cause her to come out to see you more than the other way around.
But if you get upset at her, yell at her, she's going to close you out. If that's the case, there is no relationship anymore.
If you want to be Alpha, start looking into options so you're not focused on her as much, and maybe just see her here and there. Right now, you are free to date anyone. You don't have to be exclusive to her even if you get back together with her.
You're just starting to learn about relationships, and the first one you fall for is the hardest to get over. I had a harder time getting over my first relationship than I did my divorce, mostly because I was able to cope with it a lot better.
If you're a jealous person, you're going to have to work on
inner game.
So, be able to let her talk without getting upset, even if it's about cheating. Just take a breath and let her finish.
It's okay to cry a little bit but don't have a breakdown, don't get mad, just realize that it's better to move on with the truth on the table and thank her for being honest with you.
This might lead to having sex with her. Maybe as "goodbye sex" or "makeup sex". Use protection. You don't need to mess up in a moment of weakness. Plus if she has slept with someone else, you don't need to take any chances.
If you do get back together again, let her know that if you both break up again, this is it. Not in a threatening way, just "I don't want to be an on again off again couple".
See what else is out there. You have changed and don't feel as confident in her. There might be someone closer and even better.