Hi, I'd like to help you with your question.
It sounds like your friend was hurt by your absence. Did you know ahead of time that you could not be there? If you waited until the last minute to tell your friend you could not make it to her wedding party, she may have felt that you did not want to be there.
It is understandable she would be hurt. But as your friend, she should try to understand that you could not make it to her party and that you are sorry. An explanation and an apology should be all that is required.
Since it seems she still feels hurt, then I would back off and give her time. The more you apologize the more leverage it gives her to continue to be angry. And if she tends to be an unforgiving type of person, apologizing more than once is going to fuel the fire.
Give her a week or two to cool down. She may also be upset because of the stress of the wedding, so it may make her more prone to emotional responses to problems and situations and less able to handle stress. When you feel you want to try again, contact her. Let her know you miss her and would like to see her. When you do see her, say "I hope you know that I mean the apology I gave you." and see what she says. If she is still upset, let her talk it out. But at some point, she is going to need to let this go and either forgive you and return to your friendship, or move on. If she does choose to move on, then you know that the friendship was not a meaningful and deep one, at least on her part.
I hope this helped you,