Help?

I'm bisexual as well, leaning towards a higher attraction to men. So, I have a very similar situation as yours.
I would argue you're normal, but it really depends on the definition of what normal we're going at. In this case, it probably just means being heterosexual because there's a larger population of heterosexuality. Normality is not always possible to conform to, as such with sexual orientation.
....Um, lets not dwell on normalcy too much.
The simple fact is, 你 can't satisfy everyone. If you're normal, 你 will still not satisfy everyone. Someone will always dislike you. That is...considered normal. Biphobia is a huge issue. The fact that your family accepts 你 makes 你 somewhat luckier than most LGBT people. I would try to find 老友记 that are also in the same situation as you, that way 你 can share experiences among each other. Do not ignore your sexual orientation, accept it. Ignoring your true self brings consequences and inner pain. I can't really prove that, but 你 can trust me on that. I would advise 你 not to self-harm. 你 can still lead a good life. Focus on your talents, and pain will slowly flow away.

Being normal is being who 你 are. Society doesn't need to like you, only 你 do. And whenever 你 feel like self harming, write to me and I will chat with 你 when I can. Also, your 心 chooses who 你 爱情 so let it. If it so happens to be a girl that is fine, as long as that is what 你 want. All of us just want 你 to be happy!:)