Will athlete's foot affect my toenails?

It can. Very often the cause of nail fungus is caused by athletes foot.
It can. Since it is a fungus it could be spread to your toenails.
Yes. Some fungi can infect more than one part of the body. Trichophyton rubrum can cause athlete's foot fungus, toenail fungus infection, and jock itch in the groin. This means that treating athlete's foot fungus is a wise idea, to help prevent the fungi from infecting the toenails.