How can I convince my parents I didn't drink?

Your parenst aren’t upset because they care about you, they’re upset because they’re parents and untrusting pretentious grown-ups and think that they’re always right, constantly deserving of respect, and when you deny the fact you were drinking they’re insulted because you’re going against what they so stubbornly think and are ashamed of you. If they refuse to trust you, to hell with them, and tell them that.

Be completely honest and admit to the mistakes you did make. Don’t try to bury the problem with excuses. They shouldn’t kick you out. That wouldn’t really be “legal”.

When you’re telling the truth and someone doesn’t believe you, that’s basically “on them”. Make sense? Keep walking in the truth, stand behind your truth. If they choose not to believe you and kick you out of your house, you call Child protective services on them and share your story.

They don’t trust you for some reason. Maybe you lied to them in the past about other things. Maybe they don’t have faith in you. Maybe you can ask them how you can gain their trust.

Otherwise, stick to your guns and protect yourself if they toss you out–then they are in the wrong and there are agencies out there to protect children. Use them.