So, you don't ever have to use any words for yourself that you don't want to, for any reason, or even if you have no reason. You also can not use a given word or term now because you're not comfortable (or again, for any or no reason) and change your mind later and use it if you want. And if you're not using that word because of biphobia or homophobia you have internalized, or that you don't want to live with, you get to do that. I just want to make sure you know all of that first and foremost and have that affirmed.
Alas, while you get choices about what you say or call yourself, none of us gets choices about what we feel: our feelings are going to be what they are. So, since it sounds like you're having a lot of uncomfortable feelings, including a lot of fears about acceptance by your family, it seems to me like that's the more important place to start talking and to see what we can't do to try and help you work through before we get to identity words. What do you think?
Never doubt that a small group of thoughtful, committed citizens can change the world. Indeed, it is the only thing that ever has. - Margaret Mead