Rather than assuming it is one thing or the other, and rather than pushing
your baby's limits given her reactions already, I would suggest getting a
RAST blood test as soon as possible (for both dad and baby).  From one blood
sample they can test for whatever specific food and protein in the food they
suspect might cause the reaction.  Since milk allergic people often have
other common allergies (wheat, eggs, nuts, etc.) the doctor can test for all
at once (soy is also quite common).

My pediatrician dragged her feet for maybe 4 months even though my son had
severe eczema which obviously worsened with exposure to milk/dairy, and some
other things.  He had already started vomiting violently after eating certain
foods and losing weight (10-20% of his body weight) when I 'convinced' her
to refer him out.  He was positive for all grains, all of the abovementioned
foods and most legumes-- possibly anaphylactic to nuts and eggs.  People for
some reason don't 'believe' allergies are serious but treatment is urgently
needed.  Once we removed my son's allergens, he got a LOT better and I can
tell he is healing after months of repeated exposure.

Statistically, babies of 1 allergic parent have 40+ % chance of having the
same and other allergies; if both parents have the odds are 65%+ .  No
doctor would ignore these odds with other illnesses.

Good luck!
Susan.