"Pinched nostrils" refers to the act of squeezing or pressing together the openings of your nose with your fingers, usually to block or reduce the flow of air through your nostrils. Full definition
«But whatever their China business models, the IT executives will likely succumb, even if with pinched nostrils, to Lu Wei's and Xi's siren song.» (fortune.com)
Tilt your head forward and pinch your nostrils together just below the bony center part of your nose. (kidshealth.org)
Place gauze or tissues on the nose and gently pinch the nostrils closed with minimal pressure. (wehavekids.com)