This is an extremely irritating, annoying, snobby child who demands their way at all costs, even to the point of embarrassment. A more acceptable term for a brat. May also be used as an adjective
"That snotnose got us kicked out of saks" said the babysitter to her friend, " now I have to shop at macy's, eww"
that snotnosed bitch got me to do her chores!