You might try a second opinion for Fiona. Those two antibiotics are fairly common for URI's and fairly potent. It's possible there could be another cause for the URI or it just needs more time. I'd try picking up the prescription and if that doesn't work seek a second opinion if it was me.

Animals can have athsma just like people.

And like people sometimes environmental things can set them off. We have a dog that visits our hospital occasionally who has had a bad cough for about a year now. We did everything medically but the dog coughs because of environmental reasons, his owner drowns himself in cologne!!! I'm not kidding this guy can walk in the door, be in there less than 3 minutes, walk out and we can STILL smell his cologne 4 hours after he's gone even with the windows open and the fans on!! So strong odors (purfume, cologne, sprays etc) can cause coughing from asthma.