Coughing, wheezing and breathing heavily is not something we could diagnose or treat on the forum. It could be a disease or some infection & would need vet to diagnose & treat as that is rather serious especially in a fluffed up bird.
Were they exposed to any chemical smells, cleaners, paint scented candles???? That too could affect breathing.
If so air out the area.
The droppings though I am not a canary expert don't seem to show much.
Keep the bird quiet & warm. Clearly the bird is in distress & don't usually show this until they are very sick.
My advice would be to contact a vet.