What part of my organs is located to the right of my belly button and what could local hardening/swelling mean?

Hernia, Appendix, : The sensation you are having could be many different things. It could be a hernia, or a lipoma – which is a benign fatty tumor under the skin, appendix –. Unlikely because it would be very painful, abscess or cellulitis- a skin infection that requires prompt attention & antibiotics. If the skin is red, swollen then it is a skin infection. In this case you need to see a doctor promptly.