You can find the ingredients on cosmetic products (shampoos, soap, sunscreen) and search for carcinogenic (known or suspected) or harmful ingredients on https://www.safecosmeticsact.org/search.
It's run by the California Department of Public Health, which gives public access to their database. By law (passed in 2005), manufacturers that sell cosmetic products in the state must report the ingredients. Yay, California!
The user experience is not great, but at least the information is public. Hopefully, someone with more talent for designing web and mobile apps would create a better way to get these data.
