Lena, I personally still get runny noses when I drink cow's milk. I am told that in some individuals it produces excess mucous and then the runny nose. I generally have given up milk, but sometimes can't resist. As I am an adult and not a child though, I haven't a clue as to what to do for a little one. Except that if I were in the same situation, I probably would refrain from the milk. I know I can make the choice to drink milk and deal with the runny nose. not sure what purpose it would serve your ds.
My .02 not based on anything the medical community might have to say.