That is young, to expect her to wipe herself... consistently.
Me and many of my friends, were still wiping their kids at this age.
It is not unusual.
And yes at this age, they don't always do it... nor are they good at it.
Teach her to wipe from front to back, although I'm sure you taught her that. And teach her why.
Also, washing her down there with some soaps, will actually be the cause of infections... bubble bath also causes UTI's in girls. So, don't wash too briskly down there... but use your hand or a soft cloth, but don't "rub" vigorously etc.
-yes, "baths' are more infection causing. Showers, are better. If she is at the stage/age where she can do showers. But probably not...
Also what can cause a sore red bottom, are acidic juices.
But yes, not wiping, can cause smells or bacteria build up down there/moisture build-up... and thus yeast infections and/or infections.
But still, you need to wipe her still. And after going poop too.
A 3 year old can't do that real well yet.
Especially after pooping. That is hard for even older kids, to wipe cleanly and without residue or skid marks being left behind.
good luck,
Susan