Which of the following symptoms would suggest an animal may be sick?

Symptoms such as nasal discharge and vomiting are significant indicators that an animal may be experiencing illness. Nasal discharge can suggest a respiratory infection or allergy, while vomiting can indicate various issues ranging from gastrointestinal problems to systemic illnesses. These signs reflect a deviation from the animal's normal state of health and may warrant veterinary attention for diagnosis and treatment.

The other options illustrate behaviors and conditions that typically indicate an animal is healthy. Playful behavior and a good appetite are signs of well-being, just as bright eyes and shiny fur indicate a healthy state. Sound sleep and normal activity are also positive signs, suggesting the animal is not experiencing any distress or health issues at that time.