I tried doing just milk. I felt better than with most foods, but yogurt makes me feel a lot better than milk.
I think the lactose has something to do with it, since I find myself to be sensitive to other sugars.
It get's all very complicated, of course. Turning milk into yogurt can also change the proteins' shapes, so that might make the proteins less of a problem.
You must have a lot of discipline, so you can try lots of experiments: Lactaid (with lactase in it), acidophilus milk (like yogurt but stopped sooner), whey versus casein, sugar alone if you dare.
Lactose intolerance has very specific symptoms. But if the problem is sugar, think about how yeast makes bread rise a lot more when you add sugar. They love it.
I used to make yogurt regularly, and sometimes let it go on much longer than recommended. It gets very sour, which means that there is even more lactic acid in it and so there is less lactose. Regular yogurt still has some lactose in it, because if it were very acid-tasting people wouldn't buy it.
You can make your own just by using a tablespoon or two of yogurt that you buy and stir that into milk. (That's also a way to discover if the "live cultures" in it really are still alive.) The hard part is keeping it up to the correct temperature range so the good bacteria can grow. You'll notice that the milk doesn't go bad, you don't even really have to cover it. It's very impressive how the good bacteria keep the other ones down.