In an apology, one says "I'm sorry I did X." Period. "I'm sorry I was rude". One accepts responsibility and does not try to blame the other person in any way.

When you said "Not everything is about you" you took away the apology, you made it seem like you thought things were her fault.

A proper apology would be to say in a calm and sincere manner "I'm sorry that I was rude to you."

No excuses such as you didn't know it was rude. Whether you knew or not, it was still rude and hurtful. No blaming her, like saying she should have responded differently.

Just this, said in a calm and sincere way: "I'm sorry that I was rude to you."