Lactose intolerant ??

When we went for my daughters 1 year check up, I mentioned that despite my attempt to transition her on to milk extremely slow, she still seemed to have really bad diarrhea. Her dr told me to try again, if whole milk doesn’t seem to go well, try 2% if that doesn’t go well, try the Lactaid (I believe that’s what it’s called). Well it’s been over a month and I feel like she has way more diarrhea poops than solid ☹️ So I think I’m going to have to try the lactose free milk. Does anyone have any experience with their little one being lactose intolerant? I know she hasn’t been tested or anything, but should I cut out all dairy or just start with the milk and see how she does?