sneeze
嚔 centers on the act of sneezing. It is a specific character for that bodily reflex.
嚔 combines 口 (mouth) with a phonetic component that likely represented the sound of a sneeze. The exact historical development of the right side is uncertain.
The left side is a mouth 口. The right side looks like a complex sneeze exploding out: imagine the shape as a burst of air and sound from the mouth.
For テイ, picture a sneeze so powerful it sounds like a loud 'TAY!' bursting from the mouth: TAY -> テイ.
to sneeze