I have always been told the opposite, that allergies do run in the family. All doctors believe different things though. I have been told that if your child has a sibling or a parent with a food allergy, it is best to avoid that food until 1 years of age (to be safe).
Example: DS1 could not handle milk products (not even cooked in foods) until 18 months old. I am avoiding ALL dairy, even cooking until DS2 is 1 years old and then I will try it very slowly.
If there is no real known allergy (sibling, mother, father) to milk and wheat, then I think you would be okay.
When you cook with whole cows milk, it does break down the protein, so I think you would be okay.
Also wheat is in many of the teething biscuits and those Gerber puffs for finger foods.
All you can do is try and it you notice any type of reaction, then I would stop and try again at age 1.
Just watch for gas and stomach cramps also, not just eczema, hives, etc.
Hope this helps, Wendy