While it’s not 100% fool-proof, the easiest way to test for a dairy intolerance is to take note of how you feel after you eat dairy.  Eliminate the dairy from your diet entirely for 21 days.

This means more than just not drinking milk with cookies.  No dairy of any kind.  No cheese, no ice-cream, no whey protein shakes; total elimination.  After three weeks see how you feel.  If there is an improvement in symptoms, it is likely you have a dairy intolerance and you would want to consider continuing to eliminate dairy.