Ruputured Appendix

I went to the Doctor for severe stomach pains and he sent me to the hospital for out patient tests.  At the hosptal they did an Ultrasound on my stomach and found nothing unusual.  The pain continues, so I go to the emergency room and they look over the "ultrasound" (was done earlier by the same hospital) and a CAT scan and a MRI of the stomach and the Doctor said he could not find cause of pain.  His nurse did tell me before we left that their was a small Kidney stone in each Kidney, but that was not probably causing any problems yet.  Also, the Gall Bladder has a "sandy sludge" in it.  I went home and that night the pain got worse.  I could hardly walk or even move because of the pain.  I thought I may be passing one of the  stones.  At about 9:00 I went back to the Emergency Room and they found that my Appendix was ruptured (different Emergency Room Doctor).  How did they miss the problem with the Appendix the day before?  Did it take it becoming ruptured for them to diagnois it?