Although I can't relate exactly or help out much with your situation, I know what its like for your family to think you're gay. My family thinks that, particularly my mom and brother (my dad's not in my life enough to notice/care), possibly because I have never had a boyfriend, I'm not very girly, and into rock music and martial arts. I am bisexual so they're not completely off.....and now my best friend is gay. That REALLY didn't help. lol.
Really all you can do is tell them you're not gay, if I think of more advice I'll definitely let you know. Until then good luck, and I hope things go well with whatever you do