This same thing happened to me a few years ago. Discover card called me to ask me about some new charges on my card. It was over $2,000 that was charged, all online for clothing. Since I never do that, Discover was suspicious. I didn't have to pay for any of that either.
A co worker had his identity stolen ten years ago and is still having to sort it all out. As of right now, I am paying all my cards online and some are on auto debited.
Have you had any problems with the things I've mentioned and if so, did you continue to pay bills online?