No. You’re not having a mid-life crisis (you haven’t even hit a quarter-life yet). What you have hit is puberty. Different people respond to the hormonal shifts of adolescence in different ways. Some girls act as you do. If your mum didn’t have the same reactions to puberty when she was young, she might not understand that it’s your hormones that are talking, not you, when you go off.
I strongly suspect that your moodiness and irritability have to do with adjusting to the emotional rollercoaster that often comes with changes in body chemistry during the teen years. You might tell your mum I said so. It’s clear to me from your letter that you do love your family and want very much to show your appreciation and respect for your parents. You are as surprised and upset about your own behavior as they are. A book that you and your parents might find helpful is: I’m Not Mad, I Just Hate You!: New Understanding of Mother-Daughter Conflict by Roni Cohen-Sandler. If that doesn’t give you enough help, you might want to see a counselor who specializes in working with teens and their families. You need to learn some new ways to manage your feelings. Your parents need to learn some new ways to work with you so you all come out of the teen tunnel as friends.
I wish you well.