to me all 3 are interchangeable, and a girl can be all 3, but generally speaking is either one or another. either one can mean your beautiful though, and doesn't mean one is more attractive than the other, but if you had to pick...
cute is more along the lines of having adorable, girl like (but still grown) features. like a fuller face, wide eyes... you know it just gives off a cheek pinching vibe
pretty is more gentle, and motherly looking. its a plain beauty with a soft, tender face with a warming smile.
sexy is laid back with lazy or suggestive eyes with a penetrating gaze. it can come with a sly smile with an overall look that can be hard to read with constant stone expression
I would post examples but got lazy