Left mouth radical - the indexing component, drawing the throat that gets blocked. Anchors 噎 in the family of swallowing/eating verbs with 吞 (swallow), 咽 (gulp), 吐 (spit). The mouth on the left is essential: choking is an event of the mouth and throat.
Right side 壹 - the formal banking form of 'one' - provides the sound yī, which shifted slightly to yē. A useful mnemonic: 'one mouthful too much' equals 噎 (choking on food). The image of a sealed jug inside 壹 reinforces the blocked-throat sense.