Hello & welcome, I am Dr. B, a licensed veterinarian and I would like to help you today.
Now if the dog was diagnosed with a viral airway infection, this won't be something the cats can catch. They often will develop these signs with feline specific viruses. Though we can also see some species spreading bacterial agents (though the common ones tend to be uncommon in cats and very severe when present) or it is possible we have an allergy irritating everyone's respiratory tract.
With this in mind, as long as we aren't seeing breathing distress nor snotty/green/yellow discharge from the eyes or nose (a sign of bacteria and indication for antibiotics), we can try some supportive care. To start, we can treat the affected kitties with h steam treatment. To do so, you can take them in the bathroom while you run a hot shower. The steam will help loosen and clear discharge from the airway. You can also use a baby nebulizer, but often they don’t like things held up to their faces. So, if you find that to be an issue, you can make a little ‘steam tent’ with them in a carrier (one at a time), the nebulizer next to that, and a bed sheet over both.
Furthermore, if they are building up mucus that the steam isn't shifting, use a cotton ball moistened with warm water to wipe away crust and mucus. As well, non-medicated saline nasal drops (ie Ocean Mist or Little Noses) can be used. To do so, just tilt the head back and drop 2-3 drops in one nostril. Not a favorite, but it helps. After the drops go down, you can let the head up and wipe away any discharge that gets loosened. Then repeat with the other nostril.
Making sure these kitties are getting food and water is important, as congested cats who can’t smell their food often won’t eat as well as they should. Therefore, if need be, try offering smelly wet foods (since they are high in water). It may help to warm it up a bit in the microwave to help them be able to smell it.
Furthermore, since feline herpes virus is a suspect, we can also start OTC L-lysine. This is a nutritional supplement that can help them recover quicker. This is available over the counter at vets, pet stores, and even online. They come as gels, powders, and as crushable tablets that can be mixed into food. An average cat dose is 500mg a day.
As well, for allergic concerns, you could try a low dose of an OTC antihistamine as well. Most commonly we use Benadryl/Diphenhydramine (More Info/Dose @ http://www.petplace.com/article/drug-library/library/over-the-counter/diphenhydramine-benadryl). A low dose (ie. 0.25mg per pound of their body weight twice daily) can just be enough to reduce allergic irritation. Alternatively, we can use Cetirizine (just 5mg for a cat) once daily. For either, we like to keep the dose low, to avoid drowsiness. Of course, double check with your vet first if your wee ones have any known health issues or are on any other medication you didn't mention.
Overall, this does sound highly suspicious of an upper respiratory based infection but allergies cannot be excluded. So, do check your home for any new powders/sprays/etc. being used as these may need to be discontinued. Otherwise, we'd want to use the above. Though if these signs linger or are severe, then we'd want the local vet involved to confirm our concerns and dispense cat safe decongestants (since human ones are toxic for kitties) +/- antibiotics to help us nip this in the bud.
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