How do I know if my 3 month old is lactose intolerant?

My 3 month old has been on soy formula since he was about 2 weeks old. He was taken emergency c section too early and his digestive system was really sensitive and he was constantly constipated. We tried to switch back to normal formula with no luck. He had bad tummy aches, diarrhea and projectile spitting up!! How do I know if he's lactose intolerant?