Fungal infections of the nail are caused by various species of fungi that live in the soil and in moist environments like bathrooms and shower stalls. Although nail treatments are sometimes associated with fungal infections of the nails, these are usually major treatments like the application of nail gels in a salon (here the fungal infections are either caused by contaminated manicure instruments or by creating a space near the nail that allows fungi to grow). Nail polish, like what you have been using, does not usually cause nail fungal infections. However, if you already have a fungal infection, painting the infected nail with polish will seal the fungus in and allow it to grow better. Therefore, I suspect that you may already have a fungal infection smoldering in the nails and that it is just worsened by applying the nail polish. In fact the 'brittle nails' you report may be a sign of an underlying fungal infection. Probably the best first step is to visit your primary care doctor
or your dermatologist
so they can take a good look at your nails and decide if there is evidence for a fungal infection and, subsequently, what treatment option to pursue.