Nicki Minaj had an over-the-top nose job. She had the plastic surgery in her early 20's before becoming famous. Her nose used looked totally normal, but now it's thin and jagged. It actually looks like she's close to having a Lil' Kim caliber nose - which is why it's a good thing she didn't make it any thinner. When she's scrunching her face like that, you can see just how oddly shaped it is.
You can see how thin Nicki Minaj's nose is in the right light.
Someone needs to tell her to stop making that face.
Nicki Minaj's plastic surgery was definitely over-the-top. You don't really notice how thin it is on TV, but in a still picture with the right light, it's overwhelmingly obvious.