Picking your nose in public is considered rude.
However if you do need to pick your nose in public most people won't care that you do so as long as you don't wipe the boogers on something.
Just make sure you wipe your hands and wash your hands after picking your nose and put the boogers in a tissue.
Or better yet wait until you're not in public such as in a bathroom etc to pick your nose.
However it's also okay to wipe your nose in public and blow your nose in public as long as you're doing so in a tissue and you're washing your hands afterwards.
Just don't touch things in public that others will touch after you have had boogers on your fingers.
That is unsanitary and gross.