In is episode Diana's sister, Minnie May, is suffering from croup. Croup is more commonly known today as bronchitis.
Croup is caused by swelling of the upper airway. Steam does help loosen the mucous and cool night air reduces the inflammation. Although croup is usually mild, it can be quite serious on occasion. Raw onions were used to treat a variety of ailments at the time, but there is no medical evidence for using them on the soles of the feet. Croup is not the same as asthma or bronchitis which are inflammation of lower airways.
The title is a quote from 'Jane Eyre' by Charlotte Brontë.