Are most people that are allergic to dairy, also allergic to soy?

My daughter has eczema. After having an allergy test, I was told she's allergic to dairy. We took her off of dairy and she's been doing pretty well. Then we introducted her to soy milk. Last night she was up all night scratching. I was wondering, if most people that are allergic to dairy also allergic to soy? The allergist didn't mention anything about the soy, wouldn't they have tested for that?