Lactose intolerance gives you an upset and very sore stomach, but not eczema.
MSPI gives you eczema and watery / mucousy / blood in the / poop, plus bloating and excess wind.
MSPI is more common than lactose intolerance in infants.
The only way to know for sure is to try lactose-free dairy products and see if things improve or get worse.
HH