"Look around the web and you'll find countless references to "feed a cold, starve a fever" being a misinterpretation of a line in Chaucer's Canterbury Tales that reads "fede a cold and starb ob feber" which is translated as "encourage a cold and die of fever." - i.e. a cautionary message that if you allow yourself to get a relatively minor cold you could contract something much nastier."
https://www.bookbrowse.com/expressions/detail/index.cfm/expression_number/523/feed-a-cold-starve-a-fever HERE

May be she don't take no tea for a fever cause it's BS to do so?

Opinions vary : feed a cold, starve a fever

Also, there are more then one type of fever : the white hand of a lady fever thee

Rest her soul