Could dd have a dog allergy?

[Piffle]

WE got our puppy a week ago
DD is 2, our pup is pretty much confined to kitchen and outside. But DD has petted and played with her quite a lot through the days.
DD now has runny nose, runny eyes and a night cough that now sounds wheezy/singing
I had asthma as a kid and it reminds me...
Pup is very shorthaired but am really worried that it could be an allergy.
We have a cat who dd will fair carry around no symptoms there as we have always had cats
Ring a bell anyone or could it be a cold? The mucous (urgh) ir very runny and clear and dd sounds like she has lots of catarrh
Gross sorry... DD is otherwise a non snotty child...

Would have thought it strange to be allergic to a dog and not a cat, the allergy is usually due to saliva and cats lick themselves more. But I imagine you could be allergic to dog hair, perhaps see if cold develops firt though.