Relationship problems
The Man's "job" is these kind of situations is to first decide if its worth it to continue on with this girl.
Was this totally out of character for her? What was the outburst about? What caused it?
It is not unknown for a woman to lose control of and be guided by their emotions. This is is what they are after all. Women have childish outbursts all the time and often do not apologize for it (sometimes they do.)
You have to decide if you can expect to see more of these kind of outbursts in the future. You have to decide if your woman is simply a nutcase or doesn't respect you or doesn't actually care for you or is setting things up to break up with you.
If you do decide she is worth it, the Man's second "job" in these cases is to find a way around the problem for both of you without either of you losing face. Especially for you. Women's emotional nature makes this very hard for them to do. Men's pride sometimes makes this very hard for them to do as well.
But this is the kind of guy that women are looking for. A guy who will find ways around problems like this without sacrificing his self-respect and without making her sacrifice her self-respect as well. A guy who can balance off her emotional nature and be The Man in the relationship.
In this particular case, she has already said that she won't apologize. So don't make her. You obviously have nothing to apologize for, so don't.
She thinks she had some kind of "right" to have this childish outburst. Women often feel this way, that they have a right to their emotions and the guy should not be able to discount or ignore them. So you have to concede her "right" to have lost it.
But you also have a "right" not to concede that it was your fault. You also have a right to ask that this kind of thing not happen again in the future (or rarely that is, see women's emotional nature again.) You also have a right to tell her what you "expect" from a woman you put an effort into.
You have both decided to wait each other out for that first phone call. I might wait a day or two more and then make the call. I'd smooth things over mentioning those points I made above.
You should be calm, cool and collected when you have this discussion, not angry, not wussy, not emotionally. This is also what a woman is looking for in a Man in these situations.
This kind of thing often happens at the two month or three month mark in a relationship. It is a "test". It is a "relationship skills test". Women don't even know they are doing it when it happens. They are compelled to. You pass the test by first deciding if this girl is worth it. Seondly, you find a way around the problem without losing face for either of you.