Health Effects:
"Ingestion: May cause irritation to mouth and throat. Nausea and vomiting may be seen with large ingestion. Waxy products (sticks) may cause diarrhea."
What to do:
"Ingestion: Rinse out mouth and drink a small glass of water or milk."

http://www.dpic.org/faq/deodorants-and-antiperspirants

I'm sure you will figure out the best way to handle the situation.