Sinus and upper respiratory tract infections, including kennel cough (tracheobronchitis) are very contagious, and can be easily transmitted by aerosol in any environment where dogs can congregate in groups, such as kennels, puppy day camps, dog parks, in multiple dog walking situations, and during hospitalization, etc. Dogs even have their own "common cold", which is viral. But a secondary bacterial infection can also be implicated.
It would be best to have them both examined by your vet, especially since your King Charles is not eating. Shaking their ears could simply be a bacterial or yeast infection (otitis externa), which may be related to the upper respiratory infection, via a sinus infection, or it could be coincidental, if both your dogs are prone to allergies.