Is it possible for high heel shoes to stunt your growth?

No. But if someone is still growing it might be favorable to keep their feet in a more normal position during development. Too much high heel wearing can also cause the achilles tendon to contract and shorten, and also places stress on the knees. Everything in moderation, in terms of amount of time wearing them and height of heel.
Absolutely not. Shoes have nothing to do with how your foot grows.