Girl who may feel badly about public relations (5)

I believe the answer is:

april

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'girl who' is the definition.
'April' can be an answer for 'girl'. I'm unsure of the remainder of the definition.

'feel badly about public relations' is the wordplay.
'feel badly' becomes 'ail' (I've seen this in another clue).
'about' means one lot of letters goes inside another.
'public relations' becomes 'PR' (abbreviation).
'ail' going around 'pr' is 'APRIL'.

'may' acts as a link.

Can you help me to learn more?

(Other definitions for april that I've seen before include "Month to be in England (Browning)" , "Calendar month" , "Fourth month" , "Month of showers and of the Queen's birthday" , "Part of spring" .)

I've seen this clue in The Globe and Mail.

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