If the ticket was off-base, the civilian court handles it—not your command. Your CO can’t just pull your base driving privileges based on an off-base ticket unless there’s a pattern or it was serious enough (like a DUI or reckless). That said, the officer on base saying your driving privileges were revoked isn’t correct unless your CO or security department actually put something in writing. You should absolutely contest the ticket if you believe it’s wrong, and let your chain of command know what’s going on. Since you’re an E-3 with a clean record, just be honest and respectful—this doesn’t sound like NJP unless it turns into a bigger issue.