Hi there. Big big (((((hugs))))). I know it can be so worrisome and so frustrating trying to sort this all out. We'll certainly help you try.
First, great job making the dr take a stool sample. It's so hard to advocate for our LOs sometimes, and good for you for listening to your instinct. Turned out to be very beneficial.
In answer to your question - YES, milk allergy can absolutely cause blood in the stool. That's exactly what happened to my DD2. She had loose, mucousy stool with blood in it. It was horrible. Eliminating all dairy and soy worked very well for us (along with other allergens, but she is a pretty rare case). There are some moms who can just eliminate obvious dairy (like milk, cheese, yogurt) but others have to eliminate trace dairy as well (and soy), which can be very difficult. Regarding soy letitchin, I eliminated it, but from what I understand it's not exactly necessary.
It's true it can take weeks for it to be out of your system and then out of your baby;s, however I (and lots of mamas) see big improvements in just a few days.
Although you have been eating milk./soy all along it could just now be impacting your DD to such a degree. She may actually have had microscopic blood in her stool for awhile and you didn't know. Was she fussy, had difficulty sleeping before the diarrhea? Those can also be symptoms.
Giving up the milk and soy can be very challenging, if you do it please consider seeing a nutitionist for yourself. I eventually got hypoallergenic calcium supplements from kirkmanlabs.com - they were great - but I waited too long and should have done it from the beginning.
Huge Huge hugs....hope this helps a little.