So it seems I may be lactose intolerant after all. I reacted to the cream in my hot chocolate and the morning after, I got sick to the milk I drank. I spoke to my GP about it and she said one may not react right away, but have a delayed reaction. Crap. And apparently I introduced too much at one time. I'm to introduce milk again 3 days later (tomorrow), 50ml at a time, not 500ml :) So we'll see.
Cheese doesn't seem to bother me, nor butter on my toast. So maybe just certain dairy. Maybe just milk. I still have to try organic milk after this.
Later Edit: Retract the cheese comment. Also a possible issue.