Hi, both DD2 and DS have/had cows milk protein intolerance (also wheat and corn). Unfortunately the only way to test is to eliminate ALL dairy for at least 2 weeks and then reintroduce it. Although you may see an improvement after 2-3 days it takes that long to get out of your system and your baby's. Blood tests and skin prick tests will only show positive results for an allergy.
You need to be careful and check the ingredients on all food. I use Nuttlex or Olive oil in baking, have porridge with water for breakfast etc. I recently went out for dinner and forgot that crispy skin fish is cooked in butter and the following day DS was back to screaming, waking up constantly (usually sleeps very well) and cramping. It takes him about 2-3 days to get back to normal.
My paediatrician who diagnosed DD2 said that most kids grow out of it by 3, she's now 2.5 and has grown out of the dairy intolerance in the last month. Which gives us hope for DS who is 12 weeks, (he also gets reflux when I have dairy).
I would recommend getting a referral to an allergist who specialises in children and make the appointment now as they usually have long waiting lists. If you eliminate dairy and see no change in your baby's behaviour you can always cancel the appointment.
Make sure you reintroduce dairy after 2 weeks and continue eating it for couple of days to be sure that it is dairy causing the problem and that your baby is not just having a bad day.