Sometimes, when you add a new Twitter or Facebook account, after authorization, it will not appear in your Account Management settings. In other words, you'll authorize your new account, it will appear to have worked, yet it's not visible and thus you cannot use it.
This is an exceedingly rare issue, but is nothing more than a bizarre caching issue. To resolve it, do the following:
1. Log out of Twibble.
2. Log out of Twitter.
3. Log back into Twibble.
Please let us know if you are still experiencing issues.