Should I reach out or nah?

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Hey /adv/, just looking for some advice, both guys and girls would be helpful!

Essentially, I was online dating this girl, and things were great, I flew over and had a date with her some two months back. Essentially, my school year ended before hers and she was busy. I ended up acting kinda needy since she was so busy, and I felt kinda ignored. Y'know the basic stuff, contacting too much, too many compliments, too much future-talk, general desperation type stuff. In my defense it was my first real relationship, and I was a bit too gung-ho about things, though it's not an excuse for how I acted.

Anyways, after a bit, she called off the LDR and a date we had planned in my country. Since then I've not communicated with her in around 3 weeks. It's been good for me, these 3 weeks, to kinda wrap my head around things that I'd done, and how much I had really screwed up. Now that I'm more level-headed, I'm at an impasse:

Should I try and reach out to her and try to rekindle what we had, or wait for her to contact me?

Was wondering if people think it's impossible to come back from, or if I can prove I'm changing. If it's the latter, what should I do? I've been debating starting up some friendly communication and moving from there, but was looking for some opinions from non-PUA or sappy love blog sources.

>inb4 move on