Biracial means that you are a child of parents with two different skin tones (not already classified as black or white or middle eastern or something like that.) If your parents are also bi-racial, then you can call yourself multi-racial, but honestly it really just doesn't matter.
I think you're right, it really starts with yourself. If you categorize yourself, and everyone else does too, then it's inevitable, you will categorize others, and they will categorize you. People look different, they always have. But I don't think that's any more important than where you live, or what you eat, or what you like to do. It's just that everyone makes it into this big deal, so you don't really have a choice but to make it into a big deal too.
Don't worry about race. You are human. And so am I. And so is everyone else. No worries.