Background/Context (actual question is further below):
At the end of my junior year of college in early May, I was with a girl I had known for some time, though we had only started becoming more intimate for a couple months. She graduated this year, and she's going back to her home country for 2 years to work. She said she didn't want to continue things abroad, though she did like me quite a bit. I tried to convince her to keep up a LDR (being kind of needy/clingy in the process, failing some shit tests), and she went from saying no, to yes, and finally said no again during the last few days we interacted in person.
After we ended things, I suggested we cut contact for a while; somehow, we ended up sending a few random messages back and forth. About 10 days ago, I sent her a couple messages, and she hasn't responded.
Basically, we separated primarily due to circumstance rather than a lack of attraction, though my neediness/excessive chasing (e.g. she says "I don't want to see you anymore!" and I responded "Cmon, let's meet later tonight") during the period before she left, and even a little while afterwards, probably made her less likely to want to do a long-distance relationship.
Here's my problem:
I have this massive urge to contact her again, to say that we should try things out for a few months, or just to check in. Perhaps all I'm seeking is her validation after she didn't respond to a couple of my messages - I'm not sure.
Deep down I know that if I continue to try with this girl, I might ruin the chance that she may come back and contact me (persisting will probably come off as needy and unattractive, after we agreed to separate).
I guess I want to do this to "be sure" that I'm rejected? In a way, I think it will help me get over her. Because the main reason for us separating was circumstance, I feel that if I don't persist until I get a flat-out "No." (even though that's already kind of the current situation), I'd keep thinking about ways to get her (even if deep down I know I have no chance) and that does my head in - I'm finding it difficult to concentrate on my work and studies at college...So I have this really needy urge to persist further, so I can know it's actually OVER and I can forget about the girl, to force her to explicitly turn me down in a way that I can't possibly lie to myself about.
I feel like this is just a ridiculously beta mentality, of wanting to take it too far to know you've been rejected but...It's difficult to get over my oneitis because there was still some attraction (though I know that in the end, she choose to not want to continue things when she could've).
Can anyone relate? What should I do? Do I just suck it up and move on, or ask her to try an LDR once more?