Appendicitis is a tricky one. I had a ruptured appendix when I was 7, and let me tell you, that was the most miserable I've ever felt in my life. Before it ruptured, though, I was vomiting profusely, had a fever, and EXTREME tenderness and rebound pain. My parents waited three days to take me to a doctor, which is why it ended up rupturing, but you will know something is wrong long before it bursts. They might check a white blood cell count, as it will usually be markedly elevated if you do, indeed, have appendicitis.
IBS can cause significant LRQ (lower right quadrant) pain that is difficult to differentiate between more serious and sometimes life-threatening conditions. If you find that your LRQ area is exceptionally warm, hard to the touch, and you have a fever, it's time to see a doc!