noun
blowing one's nose with one's fingers
Refers to the act of blowing one's nose using one's fingers, typically by closing one nostril with a finger and blowing forcefully through the other. Often done outdoors or when a tissue is unavailable.
ハンカチがなかったので、仕方なく手鼻をかんだ。
I didn't have a handkerchief, so I had no choice but to blow my nose with my fingers.
The general expression for blowing one's nose, typically with a tissue or handkerchief. 手鼻 specifically means doing it with one's fingers.
Compound of 手 (hand) and 鼻 (nose), literally 'hand nose'. The exact historical derivation is uncertain, but the word straightforwardly describes the action.