See here
http://www.star-k.org/kashrus/star-k11_pesach_directory.pdf page 57:
IV. COSMETICS
L’Halacha, all non-food items not fit for canine consumption (nifsal mayachilas kelev, i.e. something that one would not feed his dog) may be used on Pesach. This includes all cosmetics, soaps, ointments, and creams. Nonetheless, people have acted stringently with regard to these items. Below are several reasons why people are strict:
1. Many products, including shaving lotion and perfume, contain denatured alcohol which can be restored to regular alcohol. According to most opinions, one should not use such products on Pesach. The list notes products which do not use chometz-based alcohols.
2. The Biur Halacha (326:10 B’shaar) writes in the name of the Gra, that one should be strict and not use non-kosher soap all year (sicha kishtiya). Although we are not accustomed to this stringency, many individuals have adopted this chumra during Pesach and do not allow the use of chometz items even if they are used externally.
3. Some are of the opinion that we do not say “nifsal” (food is unfit for canine consumption) on an item that is initially produced as a non-food item.
4. Lipstick is often inadvertently ingested when eating food. If it contains chometz, it is halachically permissible to apply to the lips since the lipstick is unfit for canine consumption. Nevertheless, most women prefer not to consume even a trace of anything prohibited. The list provides chometz-free lipsticks.
5. Mouthwash and Toothpaste contain sorbitol and other ingredients which may be derived from chometz. Although, l’halacha these items are permissible to use since they are nifsal mayachilas kelev, many prefer not to use them as they are taken orally. The list provides information regarding such products.
6. Historically, it has been the custom to follow stringent opinions regarding Hilchos Pesach. In addition, it seems to have been a prevalent custom to restrict the use of items which may contain chometz, even when they are clearly nifsal mayachilas kelev.