Although I'm not from the USA, I have a little bit of idea of the US culture, having stayed there for a few years.
A year or two ago, I made a similar mistake. I had a really close friend, and I dumped my emotional baggage on her, just like you... What's more, I even snubbed her when she was trying to help me get over it.
She got angry, stopped talking to me, blocked me on social media, yada, yada... Exactly how it happened for you.
One fine day, I decided to make amends (again, just like you!). But I didn't have Interpersonal.SE back then... I had to figure things out by myself.
I tried many things; some worked out, some didn't. At first, I asked one of our mutual friends to talk to her first, so that I would at least know whether she'd want to even talk to me... (This went off very badly, don't even think of doing this...). I'd suggest a sorry email or message the very first time you try reconnecting, if there's no way for you two to meet in person. For me, it happened at school, so there was no issue with meeting her.
A day later, I went to her myself, and tried to grab her attention. She looked at me in the eye, and called me a jerk in front of everyone else. That day, I was really angry at her too. I thought that there's no use going and apologising to her anymore, and since there was no love lost between us (figuratively), there's no reason why she would forgive me.
Although I thought and felt this, my mind had plans of its own... I was always sulking, and low, because at the back of my head, I knew that I was responsible for this whole mess, and it was completely wrong of me to have gone and behaved how I had with my close friend.
When my mom asked me why I was feeling low, I told her the entire story... She told me to try and apologise again, with just a note, rather than saying it to her directly, as she didn't want to talk to me.
I wrote a sorry note, which was something along the lines of: "I'm truly a jerk... I should have never spoken to you like that. I've realised my mistake now, and if you can forgive this poor jerk that I am, I'm ready to be friends again"... I handed it to her one day when she was passing me. I gave it to her, and smiled at her once, before walking away...
The next day, I got a message from her, saying "Forgiven... What next, jerk? ;)".
Now, what I'd suggest to you is, go and talk to your friend directly first, or is that's not possible, call her first, don't send her a note/email immediately. Her calling you a jerk, or whatever, is an important part of the process. Preferably, don't get angry back at her, because it's actually her turn now, after your emotional baggage found it's way to her. You should apologise to her the very first time you talk, be it in person or not. If things don't work out, if your friend isn't as understanding as mine was, maybe it'll be the last time you talk to her, but at least you can say that you tried. There is nothing wrong with trying to contact her, but if she doesn't like it, you should not push it any further.