Is it normal to experience racism from your own race?

Growing up I was teased relentlessly by people of my own race for "acting too white." In my life I've experienced far more racism from people of my own race than I have from "white people" or other races. Now, in my adult years, I sometimes actually feel uncomfortable around my own race or even members of my extended family. I've never once wished I were white or any other ethnicity for that matter. I'm proud of who and what I am and my strong ancestors and unique culture. It's just sad for any group of people who have experienced ridicule for centuries to turn right around and direct that same hate and fear towards people of their own kind.