I suppose there might be added lactose to soy milk in the States, though I can not imagine why they would or what benefit there would be to it

but soy milk (elsewhere) does not have lactose in it. Soy is lactose free. Lactose only occurs in mammal milk.
As Eloys said I suppose it could be milk protein intolerance but if she was fine on the sensitive baby formula (by that I assume you mean a lactose-free milk based formula) then it would seem more likely to be lactose than milk protein. Milk protein intolerance generally starts out in infanthood and is outgrown in toddlers, while lactose intolerance is extremely rare as a baby and generally is something people develop as they get older but of course "generally" does not mean always and certainly could happen other ways.
I guess if it were me, I would start off with suspecting lactose as the culprit, and see if you have any changes in 1-2 months. If not, then move forward as if it is milk protein.
You can buy lactase, which is the enzyme that breaks down lactose - if your body does not have lactase naturally you can take it (or add it to the dairy product ), and then drink/eat regular dairy. Or, you can buy lactose-free dairy products which have the lactose removed. They don't really taste much different IMO.
Some people with lactose intolerance can eat regular yogurts fine, because a lot of the lactose is broken down in the culturing, but I would still remove yogurt from her diet while trying it out, and then add it back in later to see if she reacts.
Just my opinion, I am sure others have different thoughts on it though Robin! So nice to see you back here
