I agree with Barbara that these symptoms, pain, swelling, redness (and heat -
is the reddened area warmer to touch than the surrounding breast?)  do point
to an inflammatory process  the breast(s.)

  Pus can contain white blood cells, i.e. neutrophils, monocytes,
microorganisms in various stages of digestion, and altered local tissue
cells.  Neutrophils secrete acidic subsances which could coagulate protein in
milk.  But once it were coagulated or curdled could it reverse? [If you add
vinegar to milk it stays curdled.]  It would seem hard to believe that these
could be bacteria complexed with antibodies and agglutinated, but those could
be consumed by the huge numbers of macrophages in early milk.  Just
speculating.

Linda's mom with history of impetigo adds interest.  Impetigo could be caused
by either Strep or Staph but staph usually produces more pus (that is creamy
yellow.)

Even though there is no fever in Marie's mom, localized infection can occur
with no systemic symptoms.  All these other signs point to some infectious
process.  Culture of the milk and treatment might head off a possible abscess
formation.  If this started at day three could it be a hospital acquired
wee-beastie?

Mardrey