Hi Anna, I also am lactose intolerant and also become quite ill after eating any dairy products. I get chronic headaches and often vomit. I use Lactose Free Milk which you can buy in the long life milk section in the supermarkets. In WA we have two brands Harvey Fresh and Liddells, both are very good. Liddells also now make a lactose free custard which can be found in the same section as the long life milks.
I agree with you soy milk is not very nice but have you tried any other kinds of soy products. I eat vanilla flavoured soy ice cream and while it is not as good as the real thing it actually still tastes okay and is much better than missing out or making yourself sick. I also quite like soy yoghurt. I remember when I first tried soy yoghurt and I hated it. It is a really different taste but if you stick with it for a while you get used to it and actually start to like it! Give it a try and good luck.
JANE