Answers:
Yes. "Jock itch" is an infection cause by germs and fungus. Like any characteristics of bacterial infection, you can transmit it to nation by contact. The girl may very soon enjoy oral thrush or other symptoms. Both your infection and hers can be treated next to anti-fungal antibiotics. I'd also recommend visit a doctor to brand sure this is the grip, and probably an STD screening.
Of course she can be infected. You enjoy a Fungal infection ...did you report her this up to that time she go down on you? Get it checked out formerly you spread it !