You're doing the mature thing by apologizing. Even if you're not wrong. Your relationship is more important than who is right.
That said, she's not communicating with you. She's walking away and refusing to come back rather than talk it out. She's not handling this in a healthy manner.
I wouldn't worry about who is or isn't apologizing – keep doing what you're doing there. But discuss communication with her. Tell her it's okay if she needs a break from the argument, but that she needs to handle it in a different way and come back to it without you chasing after her.
You're doing the mature thing by apologizing. Even if you're not wrong. Your relationship is more important than who is right.
That said, she's not communicating with you. She's walking away and refusing to come back rather than talk it out. She's not handling this in a healthy manner.
I wouldn't worry about who is or isn't apologizing – keep doing what you're doing there. But discuss communication with her. Tell her it's okay if she needs a break from the argument, but that she needs to handle it in a different way and come back to it without you chasing after her.