I would suggest that this would be a local infection in your belly button.
No, your appendix will not show up on a US scan of your belly. They only scan the solid organs.
Do you have a fever, belly pain, and nausea and vomiting? If so, then this could indicate appendicitis. The pain would be in the lower left quadrant of your belly though.
The only real way to check this out would be to check your temp to see if you have a fever and blood tests would reveal a raised white cell count and Sed rate due to infection and inflammation. The other test, is to press on your belly and release and if the pain is worse when you release, then this could indicate appendicitis.
An infection in your belly button is most likely to be caused by the same kinds of bacteria that would cause boils on your skin.