I dunno man, peppermint contains menthol and that's very irritating to the skin and especially mucous membranes... so yeah... if I was a girl, I wouldn't put any down there at all!

It occurs to me, @mumma-monza described her discomfort like

the sensation of having the walls of your vagina rubbed with some Tiger Balm

so I think mint oil would probably be like fighting fire with fire... oh well... who knows, maybe if you put enough it'll just go numb ?! :P