Having problems with the appendix you may initially get discomfort in the belly button area, but not always.
The typical symptoms of appendicitis is pain in the lower right of your belly. You may get nausea, vomiting and diarrhea with fever. You do not have all the symptoms.
Sometimes pain or discomfort in the lower right belly area (or in the belly of children) may be due to Mesenteric adenitis which is inflammation of the mesenteric lymph nodes.
Sometimes it is hard to know if it is the mesenteric gland or the appendix that is causing the problem and an appendectomy has been carried.
If you are having a problem, it is wise to see your doctor.
An appendix that ruptures is a very serious and life threatening issue and can lead to death due to blood poisoning, also known as septicemia or sepsis.
As far as I know, the most apparent symptom of appendicitis (inflammation of the appendix) is a dull pain in the stomach on the right side, that moves to severe lower right abdominal pain.
http://www.webmd.com/digestive-disorders/digestive-diseases-appendicitis
The above website explains different symptoms that could accompany appendicitis.
If you are having any symptoms, you should probably go see your doctor if you have a family doctor, or go to the ER if you are having severe pain/think you may have appendicitis.