I have seen this question, and it is not exactly what I'm asking. Sometimes people (most especially in developing countries) raise the tip of their lips to cover their nose when a foul odour is sensed or to jeer a person. In my own language this is called 'isu imi' (To jam the nose), I'm writing a short story and I'm trying to find the best way to describe the phenomena.
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It's called "curling one's lip". That phrase does not usually imply actually blocking one's nostrils, but sometimes it does:
Even — especially — when it doesn't involve actually blocking your nostrils, it's still an expression of anger, scorn, disgust, or similar.
Swimmers call this the human nose clip.
If you can contort your face enough to do that, you won't have to wear one of these to keep water out of your nose:
Most people simply wrinkle their nose when they smell something foul.
An expression of disgust may involve everting the lips as you describe, but a person with such an expression is still wrinkling their nose.