Alicia Keys doesn't have a perfect nose by any means, but before and after pictures suggest she still had a nose job. The plastic surgery was extremely subtle and was only meant to narrow her nose a tiny bit. Before surgery, the tip of Alicia's nose was more bulbous and the bridge was wider. She was smart in the sense that she only narrowed it slightly.
Her nose has retained the same shape, it's just a tiny bit smaller.
This before and after photos shows Alicia Keys as a kid. Her nose was much bigger then, but a lot of that can obviously have to do with how she developed.