This sounds more like casein (milk protein) intolerance than lactose (milk sugar) intolerance. The reason that you can have a bad reaction to kefir, where the milk sugar is reduced, is because the milk proteins are still there. In our family several people have problems with casein. We can eat full-fat dairy (like cream or ice cream or full-fat cheese) in small amounts because the fat seems to protect us against the effects of the casein, but we do better when we avoid casein entirely. Read labels! Many products labeled "non dairy" actually contain casein as one of the ingredients. Whey, I think, is milk protein, which is why if you are casein intolerant whey will make you sick. HTH!