Anon, this happened to a dear girlfriend of mine just a couple of months ago. She, too, had a ruptured appendix, and took several days before they figured out why she was sick.
This was actually the first time I'd ever heard of someone's appendix rupturing without an incredible amount of pain, but apparently it does happen, and sepsis is the biggest threat. My friend also had a septic condition and was given large amounts of antibiotics before she could also have surgery. And when she did have surgery, they had to remove some damaged tissue in addition to the appendix.
I hope that your brother can listen to reason and not endanger his own life due to impatience. I'm sure it's frustrating for him, especially if he's having to take off work and feels like he's seemingly getting nowhere. Hang in there and let us know how it goes.