I just don't get what the problem is. Who gives a fuck about Advil? You can take like 80 of the things, and while bad for your liver, it probably isn't going to do all that much to you. Can you actually get high off the stuff? That seems inconceivable to me. And if it's just some school policy about drugs that they're overreacting to, then what the hell? You certainly don't need to stripsearch anyone for headache medicine unless there's something more nefarious at work, even if the letter of the law is that kids can't have drugs or whatever. But I don't really understand the problem. If I walked through the hall at any of my schools with 5 pounds of Tylenol slung over my back I highly doubt anyone would have so much as noticed, let alone cared if they found out.
If there's a legitimate concern that a kid is actually causing significant problems or causing harm to themselves, that's another thing entirely. "Zero tolerance" is usually in place for a reason: because kids are fucking morons who do all kinds of stupid things to themselves and their friends. You can't trust them, they don't listen to reason, they have no understanding, and they never think about consequences. People treat kids like idiots because most of them are.