Hi,
Yes, it is probable that he has the milk allergy and not MPI.....even though it was just a little bit of milk before you removed it from his and your diet, you probably have seen something in his diaper since he vomitted so quickly. Intolerances tend to present with GI and cold type symptoms. Exzema is tricky because it can be related to food allergies, but many times is more environmental.
Honestly, you kind of already started the soy trial, so if he seems fine today I would give him the bread again tomorrow.

A food allergy will usually show symptoms right away, whereas an intolerance can take days before a symptom (I.e., loose stools) show up. If he goes three days on the bread ok, I would up the ante with soy and just go for it.
Keeping everything crossed that he passes the soy challenge!! Let us know how it goes!