Final answer:
Epiglottitis is the condition that matches the given symptoms, which involve severe inflammation of the epiglottis leading to respiratory obstruction and requires urgent medical care.
Step-by-step explanation:
The infection of the epiglottis and other soft tissues above the vocal cords, presenting with symptoms of fever, difficulty in swallowing, drooling, and respiratory obstruction accompanied by inspiratory stridor is Epiglottitis. The epiglottis is a cartilaginous structure that folds over the glottis to prevent food from entering the trachea during swallowing. In the condition of epiglottitis, this area becomes inflamed, causing severe pain and potentially life-threatening obstruction to the airway, necessitating prompt medical attention.