Constipation and my one year-old

sha

Hi son has been constipated on and off for the past few months it’s the right before you turn one in he comes and goes I’ve changed his diet and increase his water intake and I’m giving him more water and I even asked us not to go to be his milk and he keeps telling me no and Im wondering if he’s lactose intolerant like his dad but his doctor said it would give him diarrhea not constipation is anyone else having this difficulty with their children