If you had appendicitis you would have severe stomach pains. This kind of pain normally starts around your belly button and will then re-locate to the lower right side of your belly and will become extremely painful. You would also have vomiting and a fever, but not normally diarrhea.
As the pain that you have is constant and dull in nature and the fact that you have green stools, would more likely indicate that you have a stomach infection. If you do, the blood tests should show a raised white cell count. You should also get a stool sample tested so that the bacteria can be isolated. This colour stool can indicate infection. Do you have a fever?