Dd has a problem with the protein in cow's milk, also with gluten. So for her the cow's milk gave her bad stomach cramps, and tbh it wasn't in her system long enough to show thru the skin - exzema. As for the gluten, after a day or two of eating breads, pasta, etc, she starts to get skin irritation on her chin, goes down her neck, covers torso. When it's really bad it goes down her legs. Takes a week to see a definate improvement in her skin, tho that doesn't mean it's completely cleared.
I never kept her on cow's milk long, tried only 3 night feeds - BT bottle. Her tossing and turning was enough for me to see it didn't suit her. I have the same prob, milk and gluten, so I wasn't willing to try it longer. So on average it's a week to clear from dd's system, or at least to notice it's going away.