I was about your age (a little younger) when I went natural. My family didn't approve. All growing up, I hated getting my hair relaxed. A few months before my 17th b-day, I decided to go natural. When I told my mother, she said that I had to do my own hair and that she wasn't going to help. Instead of chopping all my hair off, I just got it braided. Whenever I took the braids out, I cut the old permed hair off little by little. Eventually it was all out and I wore a curly afro. About 3 years ago, my mother had a change of heart and went natural herself. Now she has a a baby fro of her own. My fro has since grown and I still love it. I think natural hair is the most versatile hair style a person can have.
So, do what you want. It's your life and your body. Your mother and sister should love and respect you regardless of your hair style. If going natural is making you happy, that's all that matters. Ignore them... I definitely did.