Please help.

Well, my Best friend and I had a fight. We were in town yesterday, and were discussing where to get lunch. They kept suggesting Pizza, even though I repeatedly dicho I don't like the way some places do pizza. She called me a fusspot, and I don't know, I just got really stressed about it and shouted. She and my sister (who was there too) kept pestering to find out what was wrong, and I didn't want to tell them because some things are private. Then she just dicho she didn't want to be friends anymore. Today, I went to the park with another friend and my sister to apologise, but she wouldn't listen. We tried to discuss the argument from both sides, but she kept being immature and not listening.
I apologised, but she didn't, even though we both did something wrong. What can I do? Should I just wait for things to run it's course?
Sorry for the long question.