Her name may start with an “E”. Nuns at her school would go on about proper nail care – i.e, not showing “half moons”. Girl would also see movies with her friend by using a nickel or a dime and they had strange ratings like “A”, or “B”. May have taken place from 60s – to 80s.
One possibility is “Life With Mother Superior” by Jane Trahey. It’s semi-autobiographical, about the author’s experiences in a Catholic girls boarding school outside Chicago in the 1930s. It was the basis for the 1960s Hayley Mills movie “The Trouble With Angels.” Trahey also turned the book into a play, which can be seen at Google Books.