A.F.
Good luck! My daughter is allergic to milk, peanuts, fish and eggs. We did not realize she had a milk allergy (she had always had bad eczema) until she was diagnosed with a life-threatening peanut allergy after accidental ingestion at daycare at 12 mos old. So, here is my advice. Try a dairy elimination diet -- use soy milk (or rice milk), soy yogurt (watch - some contain milk cultures so try Soy Live -- Jewel and Whole Foods sell it), Vegan cheese (not soy cheese usually as most of it contains milk proteins like casein or whey), the kosher parve Smart Balance, and avoid anything baked that doesn't have a label and all labeled products that contain milk, whey, casein, caseinate, or anything starting with lacto- or lacti- ... it is not easy.
I breastfed my daughter for 4 mos (she never latched so I pumped for 4 mos..she is now 25 mos)-- she had the rash on her face and eczema the whole time; started milk-based formula and it got worse behind her knees, at her elbow folds, ankles, wrists; switched to whole milk at 1 yo and progressively got worse and worse...when she was diagnosed with the peanut allergy we tested for others at 17 mos (delay was because I had another baby in that time - he is now 9 mos). My daughter has now been milk-free for 8 mos. Sometimes she is worse than others...depends on how careful we have been.
You must do the dairy elimination diet for 2-3 weeks MINIMUM to see if your kiddo will get better. Dairy proteins take a while to eliminate from your system (2 weeks) then there is a delay of like a week or so beyond that to eliminate from the kiddo since you have breastfeeding. I did the dairy elimination diet with my son because I thought he had a milk allergy when he developed a rash...thankfully he did not. It is not easy. If you need any more advice -- please send me a message!
And - FYI - some kids are milk and soy allergic (I have a friend whose daughter is both) so it could possibly not solve your problem. Also, allergies do tend to run in families but not always. My husband and I are highly allergic people -- allergy shots for years. Docs said our kids have 75% of developing allergies...but they can manifest themselves in different ways (viola-daughter's food allergies -- neither of us are food allergic!).