Normally a test dose is given before the full dose. As with egg allergy, allergic reactions to cow's milk are usually mild but a few people do experience extreme reactions. Remember that recipes change occasionally. Some supermarkets produce lists of their own-brand products free from milk. Many people find these invaluable.
Some people assume that vegetarian cheese is milk-free.
This is not the case. Milk products can turn up in unexpected places. A child had a mild reaction when he ate food from a plate washed in Ecover washing-up liquid. Ecover contains a milk product. Ask for a company nutritionist.