This rare kanji has no clear standalone meaning. Treat its meaning as uncertain.
懎 combines 忄 (heart/mind) with 嗇, which likely contributes the sound. The exact historical development is uncertain.
The left side 忄 suggests an emotion, and the right side 嗇 looks like a storehouse. Picture a heart locked away in a storehouse, feeling resentment or sadness.
For ショク, imagine a shock of resentment hitting the heart: shock -> ショク, and the heart 忄 feels the sting.