Yes, schools should be able to give out over-the-counter-drugs to students because such drugs are deemed safe by the Food and Drug Administration and as such, denying them to students is asinine. If a student has a headache, allow them to take ibuprofen. It is just cruel to do otherwise.
School should not be able to give out over the counter drugs to students unless they have parental approval. Parents should teach their children not to take drugs from anyone except them or doctors. Emphasizing this to children can cut down on future drug problems. The more people you throw into the mix of dispensing medication, the more confusing it will be for a child.