Searching for my birth sibs

I've tried those genealogy sites where you type in your name and it lets you create a profile to find your ancestors and stuff. It doesn't work for me. I've tried so many times. I'm adopted, so when I enter in my name, my birth parents' names don't show up. Instead, my adoptive parents names show up. 
I've thought about hiring a private investigator, but I bet it's a lot of money. I've asked my parents for information, but all they know is my birth mom was a drug addict and an alcoholic and that I have 10 half-siblings.
I don't know what to do. I love my adoptive family so much, but I've always felt like a part of me was missing. I'm the only black person in my family. 
If anyone has gone through a similar situation, I'd love to hear it.