has your dr diagnosed her with a milk protein intolerance? My daughter is MSPI (so both milk and soy) and is bf. I've recently begun introducing goat cheese, yogurt and baked goods with milk in them into my diet, and she's been fine. the protein in goat's milk (and sheep's milk) is smaller than in cow's milk, thus easier to digest. Also, the process of fermenting (like in yogurt) or aging (in some cheeses) and cooking (ie baking) also helps to break down the protein. Which is probably why she's not having trouble when you have cheese and yogurt. She could still have the problem with cow's milk. I drink almond or coconut milk and we've just begun giving dd2 coconut milk (it's high in fat and calcium fortified) as at a year I will not be weaning her to cow's milk, and she can't tolerate soy either, and the amino acid formula is crazy expensive.
If it's a protein issue, she may have trouble with soy as well. I know some moms do oat milk too. I would try some yogurt for her directly, and see how she does, then cheese (aged cheese is better). I'd try cow's milk in your diet before I tried it in her diet. If she spits up when you have it, I would not give it to her (even in oatmeal).