Introducing it slowly sounds like a good idea. Just a note that food allergies usually show up straight away, but intolerances can take hours or days. So IF the vomitting was related to the milk (and it might not have been), it is an indication of an intolerance. This is harder to diagnose, as it doesn't happen straight away, it's not so obvious what is causing the problem. But other signs you might want to watch out for are apparent belly pain, bloating, diarrhoea and/or constipation.