I am by no means an expert on this, but I do have a ton of knowledge on milk allergies and asthma. Not that asthma is your case, but they often go hand in hand.
My grandson, whom I was raising as a baby was having a horrible time. I eventually went to making milk on my own with almonds. Soaking them, peeling the skin, blending them with water in the blender to make milk and straining the milk. I added a bit of brown sugar for flavor. But later found that goat milk was much better. We had the land and the money to purchase goats, so we did. I raised goats for 8 years.
Most think that the milk allergy comes from cow's milk. Huge misconception. It is the cow's milk but only the pasturized one that you buy in the store. Once the milk is pasturized, many preservatives and vitamins and minerals must be added to it, to make it USDA standards.
Goats milk is not expensive. Not really. It is only about $3 more per gallon than what you would buy in the store, for cow's milk.
If you could find a farmer that sells goats milk or cows milk, right from the farm, non-pasturized, you would be much better off. Goats milk is better in the sense it only takes 40 minutes to digest, but cows milk takes about 1 1/2 hr to 2 hours to digest. It's the fat content.
Nutritionally speaking goat milk is much, much better for you. I know that you can only buy the milk for animal consumption, but many that sell the milk, know this. So you must ask for it and let them know you are purchasing for your kittens or dog etc.
On another note. Check the farm out before you buy. Just like anything else. Make sure the animals are healthy, coats are shiny, and they are thrifty. If this is a route you take. I would at least think about it. You can google organic farms or you can go to Realmilk.com and check out a place in your area. Also eggs are so important. Buy free range eggs.
I'm feeling for you on this issue. It's very hard to get them healthy without good nutrition.