the throat
嗌 centers on the throat as a physical passage. Its meaning is narrow and anatomical, referring specifically to the throat.
嗌 combines 口 (mouth) with 益, which likely contributes the sound. The exact historical development is uncertain, but the structure suggests a phono-semantic compound related to the throat.
The mouth 口 is the opening, and 益 looks like a vessel with a lid. Picture a narrow-necked vessel representing the throat, with the mouth as its opening.
For エキ, imagine a throat lozenge that makes you say 'eh-key' when it soothes your throat: eh-key -> エキ.