Look at Obama at 4:11 of this video, during an interview in 1995 about his book.
Doesn’t his nose look different? Now, it might be any one of a hundred things. The lighting, the camera angle; he might have gotten punched in the nose the night before, or been in a car accident a week before, and banged up his nose. But his current nose does look different. If he did have a nose job, it may have been one of those things that is medically necessary, like a deviated septum or whatever that is.