First, the apologies. Explainations, etc. Don't make excuses for your behavior though. Accept that YOU lost control, and YOU said hurtful things. Make sure you do not try to assign blame for your behavior to what she said. Sometimes, syntax is everything.
Of course, if she won't pick up the phone, that's a problem. Don't keep calling. If you called soon after, then you're covered for not making her wait. If she didn't pick up, that was her decision. Continuing to call her over and over is just going to make her feel like you're invading her space. Ditto for trying to make a face-to-face confrontation without her permission. Besides putting her more on the defensive, this kind of aggressive strategy will just psych you up, til the first words out of your mouth are much more likely to be an accusation.
My suggestion is to leave her a voice message if you can, just saying that you are sorry, that you screwed up, and that you would like to talk. Ask her to call you, and tell her that you will respect her space by not calling anymore. If some time goes by and she doesn't call, then your best remaining option is to write her a letter. Tell her you're sorry, tell her how you feel, tell her why you think the relationship can work and can be good for both of you. Tell her that you care for her, and because of that, you understand that she needs to do what she thinks is best for her, and you will accept that. Thank her for the support, companionship, and care she has given you, and let her know that you will be there for her if she needs you. (I could go either way as to whether it would be better to mail it or to slip it under her door. Mail would be slower but safer, I think.)
Ultimately, accept that she may be right, and it may be over. She may need time alone to help herself, and you may be a bad influence, or a reminder of darker times that she can't cope with in her state of mind. And it may be what you need too. Either way, pursue your personal betterment in the meantime, and you'll be in a better place to handle whatever comes your way.