This link gives alternate names for dairy that you need to be aware of:
http://www.wholesomebabyfood.com/allergy.htm
I know it's hard when you don't have something definitive that says, "Yes, your problem is dairy," but I'll tell you the biggest motivator for me is knowing that when I consume the offending food, I'm damaging and inflaming my child's gut, making him more likely to react to other foods and less likely to outgrow the allergies he has. My other dc had a long list of allergies/intolerances and with gut healing and avoidance, she's been able to add back in many foods. My newest dc is 6 mths old and we're finding that he also has several food problems (or I should say, WE do, because the food proteins are obviously leaking from my damaged gut).
In addition to avoidance, look into healing measures for yourself. You need to do both simultaneously. Check the "resources" sticky above to learn about gut healing measures.
Personally, I'd cut out soy, too for the trial since there is such a large overlap in people that are sensitive to them.
Some subs: Rice milk, coconut milk, rice dream Ice Cream, So Delicious Coconut ice cream and yogurt, chicken stock, vegetable sauces (tomato, red pepper).
If you give us an idea of what you like to eat, we can probably recommend some ways to make the recipes dairy free.