Lactose intolerant?? Help

[Secretloverofsparklystuff]

My DD(5) is now 2,she was diagnosed with CMPA, at about 6 weeks old, (2 of my older children had it too, but grew out if it by 15months & 12 months) and settled on alfamino milk, at 18 months we moved her onto oatly. We tried the milk ladder with dieticians advice, but failed on step 1 numerous times.
Recently we started the milk ladder again, and have got further than ever before, shes managed a tiny amount of cheese on her pasta with no reaction, but when she has something that has lactose in the ingredients she reacts.
So im thinking shes now intolerant to lactose and has outgrown the CMPA?
But whats confusing me is, if lactose is in milk how come shes ok with products containing milk but only reacting to products where the lactose is listed separately?
Its probably really obvious and im being a bit thick, but i cant get my head round it.
Appreciate any help dumbing it down for me
TIA

Lactose is the milk sugar, it's hard to digest if you don't make lactase in your gut. Pretty rare for very young kids to be lactose intolerant because we are mammals that feed our young milk. But not unheard of, you'd probably have known back when you went onto Alfamino tho. Kids who'll be lactose intolerant tend to lose their lactase around natural weaning age (toddler, preschool-ish). One of mine did around 5yo.

Some things like hard cheese have less lactose because they're more processed. But they still have milk protein.

Cow's milk protein is the milk protein itself. Allergic reactions can include vomiting and diarrhoea, so it is easy to confuse the symptoms of lactose intolerance.

Have you tried lactose free dairy products? They'll have no lactose but they will have CMP. Might help you narrow down what's causing the reaction?