Why not talk to your confessor about it?
To feel that something is wrong enough to want to confess it the next day, suggests there is the sin of presumption involved.
Or, why not drop it into “Ask an Apologist” thread and see if Fr. Serpa will have a bite at it.
It still sounds presumptious to me.
What is the worst that can happen if you just get your hair cut? If you can comb it a certain way so it looks like it is cut, then the expected hair cut can not be that radical. I could understand if she was wanting a buzz cut.
Then, there is the issue of obedience to parents. Sure, it is your head and your dignity. However, provided parents aren’t asking for something radical, such as asking you to walk around with a mowhawk or bald, there should be some good exchanges, trying to be respectful of what your parents want.
I was a kid once and I thought my folks were controlling. Now that I am an adult, I’m glad they were the way they were. I learned more and turned out to be a better person for it. It was like hell at times, but I understand more now, as an adult, than I did when I was a kid.
So, just how bad is this haircut she wants?
Learning to follow God, we must learn to follow those over us. We must have reverence for authority before we can understand reverence for God. We must learn to submit to others before we can fully submit to God. Christ showed us by example. He obeyed Pilot, submitting himself to death, death on the Cross.