Note that written authorization from a doctor is needed, even for OTC drugs: "For all medicines that you are carrying, ensure that you have a prescription or written authorisation, showing that the medicine is for treatment of your medical condition"

Somehow I doubt most people have a prescription for that bottle of Tylenol or Zirtec, etc. which are a staple of the US diet. Technically customs can seize such bottles if you cannot produce the written doctor's note. In practice they wave it on, unless they have some other reason to be strict with you.