My ear piercing is infected and oozing puss, what would happen if i didn't get the puss out?

Depends: One could develop an abscess of the lobe of the ear. There is a dictum "all pus must pass". In this case an abscess would either resorb or would fester and burst. A severe infection could cause necrosis and loss of tissue and deformity. Infection, anywhere, should be taken seriously. Clean the area with soap & water, dry it and apply antibiotic ointment. Keep fingers away. See pcp if worse.

It will get worse: You must have your earing removed right away and the infection treated. If you let it go, it will only get worse and spread to the surrounding tissues.