That's a surprising statement- if it's mange she certainly won't outgrow it- it needs to be treated.
Maybe it's a flea allergy,which was your vet's first guess, but maybe it's not.The fact that it's getting larger would worry me.
It could be ring worm or mange or a variety of things- with the affected area getting larger, it would make sense for the vet to take a scraping and investigate further.