This sounds fishy to me. Apple does not sell Norton, except maybe in a box in their "brick-and-mortar" Apple Stores, which would not be a free trial. Further, a "free trial" is exactly that - you don't pay for anything unless you decide to buy it after or during the trial.
If this is actually relating to an iOS (iPhone/iPad) app, Symantec does not sell any anti-virus apps in the iOS App Store. All their apps currently are free, and the iOS store does not offer free trials.
Can you be more specific about what you downloaded, where you found it and who you gave your credit card number to?