Synonyms for Sniffle (same or very similar meaning)
WordNet sense 1 (the act of breathing heavily through the nose (as when the nose is congested)):
snivel, snuffleWordNet sense 2 (cry or whine with snuffling):
blubber, blubWordNet sense 3 (inhale audibly through the nose):
sniffFrom the ODE community, based on WordNetadd/edit