The article states they were prescription drugs. It doesn't matter if it is Advil or oxy. If the school rules prohibit the possession of prescription meds then it is against the rules to possess them. Rules are rules.
Students do have 'rights' but not the same right as others. The Supreme Court has addressed student rights in other contexts. For example, freedom of speech. Just because a student has freedom of speech doesn't mean a student can just talk out loud in class and disrupt the teaching process. The students rights are limited in a class room setting. An 18 year old has the right to bear arms but that doesn't give the student a right to bring a glock to class. The Supreme Court has recognized in many instances that the rules schools establish trump rights. Otherwise there would be chaos.
Students do have a right against unreasonable searches and seizures. The threshold issue in this case is whether the search was unreasonable. That is debatable. I do not think it is unreasonable. I had a friend in school who ate quite a bit of acid tabs when they were going to search him. Just like Sub-Zero said, people hide stuff all the time. IF the school authorities had a reasonable belief that she possessed contraband, and they has a reasonable belief that it was hidden on her person, then it is reasonable that they conduct a strip search.