Me an my girlfriend had I fight two weeks ago. She was distant and different (in fact she was stressed and had problems at home) and I told her that if she wasn't happy with me she should break up and stop acting like that.
She was upset with me but then I started acting clingy and sending text messages trying to explain why I said that (I know big mistake).Also before the fight I wanted to be all the time with her and I know she felt pressure (also big mistake and one of the reasons she broke up, I think) We haven't seen each other since and she had been ignoring me for one week and yesterday she told me she wanted to break up because she has no time anymore and she doesn't feel the same way about me anymore. I know this was my fault and I apologized to her but she said she just doesn't love me anymore but I know that's not true. What can I do to get her back??

Nothing. And do not be naïve enough to think that it was what you said or what you did weeks ago (funny that all these 'mistakes' are evident once a break-up is involved).

She moved on for her own reasons, no one can tell you those and you trying to fill in those blanks will either A) lead to nothing B) lead to you emabarassing yourself and regretting it later C) constitute a tremendous waste of time or, may fav, all of the above.

Actually, she told you why she is breaking up with you and it involves none of the reasons you mentioned. You then purport to know that her reason are not the correct reasons and that perhaps yours 'fit' better. No, no. They only fit better because if they are as you say you may have a glimmer of hope as opposed to what she has stated in which you have no hope.

Move on and away from her, friend.

We haven't seen each other since and she had been ignoring me for one week and yesterday she told me she wanted to break up because she has no time anymore and she doesn't feel the same way about me anymore.

There is your answer. Do not try and get her back. You'll be putting a lot of effort into nothing. I would suggest looking into the "No Contact" rule if you haven't already (search for it on this site, it has a lot of good tips).

If she wants you back, the No Contact Rule is a good way to initiate it, but do not expect her to take you back.
I am very sorry for your breakup, but it's best to move on now.

You need to keep your distance for a while if there is any chance at all, of you two getting together again.That means no texts,calls or brief meetings just to talk things through, in fact zero contact.

It's clear she needs space and it may be after a while things may turn around for you both, but at the moment, your relationship is clearly over in her eyes, there seems to be lots of pressure right now from various angles, you must walk away, let her be her own person and you do the same, I know it will be hard but this will get much more painful if you don't.

There is nothing that you can do right now, respect her wishes and who knows, when the pressure she is under subsides and she is able to think more clearly you just might have a chance... but she must come to you.