Sharp pain in lower right side but down near hip, close to pubic region. more likely ovarian cyst or appendicitis?

Hard to say: Nauseated? Pain duration? Quality of pain?Fever? Time of month? You should see a doctor for an exam and lab work to be safe.

Could be one of it: Some of the symptoms are common to both , beside other causes , fortunately ct scan will distinguish one from other, avoids surgery once appendicitis is ruled out, see your doctor or go to er.