I think your description of whirling disease fits my Angelfish. I just lost a whole batch of swordtails to the swim bladder infection that you mentioned, so it is possible that the angel got it from the swords, but the angel is not showing any of the same symptoms that the swords demonstrated (sinking to the bottom, bent spines, white feces, fin rot, etc.).
I am certain that when I turn the light on this morning that he will be dead, so I will remove him so that it won't spread. At least I still have one angelfish left!