You mean you're lactose intolerant?
Not necesarilly.
The symptoms are similar, but I'm pretty sure there is a difference between Cheese/Dairy allergy and Lactos Intolerance.
Lactose Intolerance is if you don't produce Lactase enzyme to break down Lactose sugars in dairy.
The Lactose builds up in the gut and causes diarrhea.
Someone who is Lactose Intolerant can't (or shouldn't) consume dairy containing Lactose, which includes Cow Milk and human Breast Milk.
But they can consume dairy from other sources, like Goats milk, or lactose-free milk (which is a procedure used to make Cow Milk lactose free).
If you're allergic to dairy, it likely wouldn't matter if you consume Lactose-containing Dairy or Dairy that is Lactose-Free. You'll still have the symptoms of allergy.
Which you'd expect to be more like other allergies, like Hayfever, or not Nut Allergy.