...consider this:

I asked a friend to buy me plain vanilla Breyer's ice cream about 10
days ago.  It bothered my stomach, even though I eat large amounts of
butter, yogurt, and cheese.  Even though it was "all natural," and free
of carrageenan, it had plenty of bean products (locust, guar, carob -
some combination of 2 or all of them).  I then purchased the "natural
vanilla" and have had no problems at all.  The one that was a problem
is called "creamy vanilla."  The natural vanilla does not have any bean
product in it.  So if you really want to know if you are having
problems with dairy, do not buy products with carageenan or these other
additives.  And I would advise avoiding homogenized and anything that
is not whole (low-fat, no fat, skim).  My stomach is about as sensitive
as anyone's, which is why I began my research into nutritional topics
when I was a teenager, in the late 70s.  Unfortunately, before the
internet, it was difficult to do much beyond the books at the local
library, unless you wanted to become a "health professional."  The
point is that I thought I was "lactose intolerant" too, which is why I
switched to a vegan diet, but now I've been eating large amounts of
dairy for over 3 years, and as long as I avoid the aforementioned
products/additives, I have no problems with it at all.