Lactose intolerance Not sure if my 2 year is lactose intolerant, but MOST of the time when I give him milk, he poops…

Lactose intolerance

Not sure if my 2 year is lactose intolerant, but MOST of the time when I give him milk, he poops right after and it's not a formed poop either. They also give milk at school during meals and this week he has pooped quite often so they thought he was sick. But he's not. My question is, if I give him Lactaid, and he's not really lactose intolerant, would it hurt him?