Wow Clint, that's some rather odd behavior from our game. I realize how inconvenient it could be to not have access to your own profile.
Unfortunately, the community can't really lend a lot of support with a technical issue of this nature, short of maybe offering cache clearing instructions.
If you continue to experience this issue, I would recommend writing into the support team for assistance. Include info like your league # and team name, as well as the browser and browser version number so that we can quickly investigate this issue. You may want to clarify where in the game you are attempting to access your profile from, and if it's the same unknown profile, or if it changes to a different person's profile each time you try.
Send us an email, and we will begin investigating this as soon as we receive it.