As we have explained in our last Halakha we are allowed to use or keep during Pesach any product which is unfit for consumption even if it may contain Chametz. See here
Medicinal pills or vitamins fall under the category of non-edible Chametz (nifsal meakhilat keleb) when they are meant to be swallowed, instead of chewed. Think about a Tylenol pill, either as a hard pill or as a gel tablet. You would not chew it, because they have a very bad flavor. Those pills were not made to be chewed (this defines 'eating' in a case of a solid food) but to be swallowed. Therefore, because you swallow the pill, it is considered as a non-edible product, even if you introduce it thru your mouth (for educational purposes only: think of it as if you would inject the Tylenol into your body). Therefore non-chewable pills don't need to be checked for Chametz ingredients. Any non-chewable pill (which is the same as saying: any pill with a bad flavor) can be taken, and obviously kept during Pesach.
Click here to see Rabbi Gedaliah Schwartz's position in OTC medicine for the Ashkenazi tradition, which follows this simple principle, but is slightly stricter than the Sephardic tradition.
OTC syrups or chewable medicine or vitamins or protein shakes, food supplements, etc. which have a pleasant or a neutral flavor, need to be checked for Chametz ingredients. Why? Because although these products are not meant as food, they are ingested in the normal way we eat food: chewing or drinking. Therefore, any chewable or liquid medicine or chewable or liquid vitamin should be checked for Chametz before using it during Pesach.
Tomorrow B'H I will present a list with this type of medicines and syrups (chewable, drinkable) which do not contain any Chametz elements.
Needless to say, in case of a serious medical condition any necessary medicine should be taken.