Which of the following conditions is characterized by toxic appearance and drooling?

The condition characterized by a toxic appearance and drooling is often epiglottitis. This inflammation of the epiglottis can lead to significant airway obstruction and is typically seen in children. The toxic appearance is due to systemic toxicity that arises from the infection, which may involve high fever and increased work of breathing. Drooling is a common symptom because the swelling of the epiglottis can make it painful and difficult for the child to swallow or speak, leading them to drool.

In contrast, laryngitis often presents with hoarseness and a cough, but does not usually cause drooling or a toxic appearance. Croup, commonly caused by viral infections, manifests as a "barking" cough and stridor but does not typically present with a toxic appearance or severe drooling. Asthma exacerbations can lead to difficulty breathing and wheezing, but the clinical picture does not include drooling or a toxic appearance as seen in epiglottitis. Thus, the presence of both drooling and a toxic appearance strongly points to epiglottitis as the correct diagnosis.