You're not gonna die just from picking your nose hairs or plucking your nose hairs however plucking your nose hairs too often could lead to a skin infection after you plucked the nose hairs.
I'm not sure if it's 100% true or not but I think I remember hearing on the DR OZ show that plucking the nose hairs can lead to the infection which could eventually lead to something with the brain.
However I've plucked nose hairs for years and nothing bad has happened to me yet so I wouldn't worry although I would try avoid plucking the nose hairs too much.
You can use a nose hair trimmer to shave the nose hair off inside your nose if it bothers you which is less painful and less risk of infection.