Masturbation since 3 years old

Hello, Im a female who is insecure of their past.  Ever since I was 3 I have been masturbating. The reason I know is because my parents would always make fun of me for it and I find it very embarrassing and gross. The masturbation never ended, I did it in public places like the grocery store and even in front of my parents.  My parents always tried to get me to stop so I only did it when they weren't around.  I have always been sexually aroused since I was extremely young and I still am, being 16. The reason I'm posting this is because I want to know if anyone had a similar past and if it's normal or if I should dread over it. Please comment