RonF:

The school has an interest in ensuring that drugs (whether OTC, prescription or illegal) are not distributed among the students outside of the control of the faculty and administration.

No it doesn’t.

No school in the United States spent a minute of its time worrying about anything of the sort until about 15 or 20 years ago, and there’s no real reason why they should, any more than they worry about whether or not students are distributing snack-packs or mechanical pencil refills outside of the control of the faculty and administration. Children can and do administer over-the-counter and prescription drugs to themselves in homes, libraries, stores, museums, parks, and just about every single other institution that they encounter in their daily lives, with the sole exception of schools. The current fixation of schools on trying to tend to every conceivable need that students might have and control every conceivable action that students might take, while on school grounds, is foolish and destructive.

It’s quite reasonable to presume that a kid might stash illicit drugs in their underwear if they don’t want to get caught holding them.

There needs to be some way of searching a kid to see if they’ve done that.

No, there absolutely does not.

If I were to grant, solely for the sake of argument, that schools ought to be concerning themselves with whether or not kids are carrying around Motrin outside of the control of the school nurse, then it would certainly not follow from that that the school has to be able to use strip searches in order to detect violations of the policies they set. Just because something is Against The Rules doesn’t mean that you’re entitled to do anything and everything in order to find out whether or not people are doing it.

Sometimes the only way to catch someone at breaking The Rules is to use procedures that would be too costly, that would interfere too much with other more important goals that the school is trying to accomplish, or that would unacceptably violate the student’s liberty, privacy, or dignity. If so, then what you have to do is just come to terms with the fact that you can’t always enforce all of your school policies all the times, and sometimes clever kids are going to manage to get away with something that the rules say they shouldn’t do — and, well, Christ, what else is new?