snivel

verb (used without object), sniv·eled, sniv·el·ing or (especially British) sniv·elled, sniv·el·ling.

1. to weep or cry with sniffling.
2. to affect a tearful state; whine.
3. to run at the nose; have a runny nose: She sniveled from the cold.
4. to draw up mucus audibly through the nose: Stop sniveling and use your handkerchief.