Should I confront a coworker who is no longer talking to me?

It's always a good idea to try to resolve an issue with a person. If you can't really remember if you did anything to make that person mad at you, I would definitely approach them with a non-confrontational attitude, and express your concern. If they continue to ignore you, you have done all that you can to try to resolve the issue like a reasonable person, and that's really all that you can do. It's always a good idea to talk things out, but remember that listening is the most important responsibility you have in that conversation.

Good luck!