Sore belly button. it is red around the button, and it smells of rotten cheese.?

An infection brewing: It seems that you have an infection there. Unfortunately, some have a very deep belly-button hole which can trap moisture/debris and can get infected. Early fungal infection can have itching to it, but bacterial infection typically causes more swelling. If an infected cyst is ruptured, it can stink. Since you are having pain, i suspect bacterial cause. Consult doc for eval. Good luck.