Hi Marie!
Just a wild guess but I think you are seeing pus in the breastmilk:  It would
hold together in "slimey clots" until swished around.  This degree of pain
and swelling just yells for antibiotic.  Doesn't matter that she is not yet
running a fever.  I have seen many cases of breast infection that are
afebrile and respond wonderfully to antibiotic.
Joanna Koch, IBCLC