Each loop in the draw is essentially drawing over itself, which is why background() is used.  background essentially draws a big rectangle on the screen to cover everything up.  But I suspect you probably want to do something like a switch() in your draw().  The case represents what screen your on.. draw this stuff...  You could also use simple if, else if, else statments.  if (screen1) { ... } else if (screen2) { ... }

Thanks, thats a pretty simple solution that I should have thought of!