How to stand up for yourself in this type of situation?

Well, i think that you should've explained the Whole situation to her and made her understand why you did what you did. And if she was still mad, then i wouldn't even talk to her until she talked to me first. Friends come and go, you can easily make new friends. Also she shouldn't have said "I'm glad we can make up by me yelling at you and you apologizing." That's not a comment she should say to a supposibly "friend". Hope this helps(: