This is a creative and relevant way to think about Socrates and what to do if you're facing an injustice. We can't tell you if you should maintain your innocence or go on YouTube and make a false confession. However, we can give you some ideas about the consequences of each.
Before you make your choice, you might want to consider if the YouTube confession is a way to escape your situation. Think about your post-confession life. In this environment, with cancel culture, call-out culture, and online shaming, it's unlikely that you'll be able to live a very "free" life after your confession. Who wants to be friends with an admitted child molester? Yes, you'll still be alive, but your friends and opportunities could be so severely limited that you might as well be dead.
In Crito, Socrates tells us "A good life is equivalent to a just and honorable one." How can you lead a "just and honorable" life if you've just admitted to something you didn't do—if you just lied?
On the other hand, are you prepared to die for something you didn't do? Why was Socrates ready to die? One reason might be loyalty. Socrates was an Athenian for almost 70 years. As the Law of Athens tells him, we
brought you into the world, and nurtured and educated you, and given you and every other citizen a share in every good that we had to give.
Do you feel similarly about the society that's accusing you of child molestation? Do you feel like they've given you an array of advantages and resources? Do you respect their laws? Would you feel bad subverting them?
Perhaps the truth of your innocence is more important than living the rest of your life chained to a lie. Then again, maybe life, however hard it might be, is more important than people knowing the truth. Maybe you won't care what people think. After all, Socrates encourages us not to care too much about "the opinion of the many."
Again, it's a tough choice: either death and the truth or life and a lie. We're glad we're not in your shoes (or sandals).