Lactose Intolerant?

My baby has been having a really difficult time passing gas and gets backed up every night poop wise. He has major poop blow outs every morning. We're thinking he might be lactose intolerant. I've been trying to avoid dairy products the last few days, but this morning he was in a lot of pain while getting rid of his gas/ poop. Anyone else experiencing this? I'm trying to avoid big dairy items like milk, but still use small items like butter. I'm wondering if i need to be really strict and avoid dairy completely. Any advice is appreciated!