Copyright and trademark infringement are the issues, and they are both bad news. Although you may or may not get their attention until you are making money, not making money doesn't make it any more legal or prevent you from getting sued.
Contact the organization and see if they have a "fan-kit" of materials they let third parties use for fan-sites, or fan art.
This is not meant to be taken as professional legal advice. Professional sports teams protect their trademarked, and not legally trademarked stuff with phenomenal zealousness.
As a gallery Moderator, I hate dealing with sports, etc. logo stuff and almost always seek Jafo's opinion on the issue.