what kind of milk is it? it may still contain whey.. either way it may not be milk at all it could be something strange or ordinary that is in his daily diet.
I am thinking if its from the hospital it is either cow, soy or donated bm for them to approve it and give it to you. The hospital will only be permitted to give you what is fda approved. most people who are allergic are to soy as well.
I was just trying to help you find other options to check into as well and very bad allergies are very similar symptoms to cf.