Lactose intolerance?

I think my 18 month old has lactose intolerance. His babysitter reports that he poops about 8-10x within the shift that he’s with her. He poops quite a bit for me as well but I’ve just never counted. He only used to poop 1-2 times a day with Similac sensitive, which doesn’t have any lactose (or little) I can’t remember. I spoke with his doctor who blamed it on his illness, because at the time he had a cold and ear infection; however, this is constant, even when he’s healthy and she didn’t seem to catch my drift at all. So my question is 1) does anyone have a child this young with food allergies/intolerances and 2) is this too young to try soy milk?

Maybe not lactose intolerance but milk allergy ****