Start by checking that the charge really posted to the credit card (and when), versus just being a pending charge when you were at the airport. Your bank or credit card company might be able to tell you the time (and date) that the pending charge hit your card and the time that the actual charge posted. Some phone agents are very confused about pending charges (aka preauthorizations), so make sure that you're talking with someone competent who understand your question and what the difference is.

Did you ever get a ticket receipt showing a ticket number for the flight or just a reservation confirmation? This wold help you to determine whether a valid ticket was ever issued.