Is it possible to be allergic to milk but not other dairy products?

I am 17, and up until recently I was not allergic to anything. However, about a year ago, I became very sensitive to milk. It makes my stomach very unsettled. I tried drinking lactaid milk, and taking a lactaid pill with regular milk, but neither helped. However, other milk products like cheese and ice cream don't seem to bother me. What do you think the issue might be?