If it is a food intolerance; I don't know the ingredients in Babycat but I would advise switching to a food that contains one protein source and one carbohydrate source, both of which need to be different to what's in Babycat. Stick with it and just that, no supplements, no medicines and see how she gets on over a week or two.

Swapping and changing won't help things, especially with her being a baby in a new environment.

It could just be the stress of the move and then swapping and changing foods has increased the problem. It pees me off that vets will just stick a needle in and give anti-sickness and anitbiotic jabs without a second thought when it's more than likely not necessary. I'm inclined to say it's probably not a food intolerance at all based on what you've described.