What's your question?
I have this really close friend that I was friends with since elementary school, but she started ignoring me because of several things I said, and I've told her I'm sorry and I'd try to do better, but she still won't talk to me like normal. Its really awkward sense we're stand partners and every time I try to say hi to her in the hallway she walks faster. I really miss her, and I fall apart without her conversation and advice, and she makes me a better person. I really want us to be friends again, but she won't let us.
This is a rough situation. Friendships can be super difficult, especially around this age. Overall, try to feel out the situation. Try different things, and if something isn't doing anything or making the situation worse, try something else. You have a few different options:
1. Give her space. A lot of times, all a person needs is some time to cool down. Hurtful words sometimes don't seem so bad after some time passes. That being said, don't completely let her go. The less time you spend together, the more you'll grow apart, which leads us to your next option:
2. Talk it out. Communication is one of the most important things in any relationship, and lack of it often leads to problems. Find a way to reach out to her effectively, in a way that you will really listen to each other. Let her know you understand it will take time for her to forgive you. Tell her you're sorry, but also tell her you feel hurt that she's not talking to you. Honesty, in this case, might really be the best policy.
3. Finally, show her how much she means to you. Let her know that she makes you a better person, and that you miss her. Give her something that shows how well you know her, or simply find a time and place to tell her how great you think she is.
There isn't a perfect solution with these types of things, so make sure to feel things out. Things will take time to get back to normal, but if she's as good of a friend as you say, things will be okay.