The most common and most likely answer to this crossword clue is the 7 letter word FEBRILE
I've seen this crossword clue in Financial Times
F
E
B
R
I
L
E
More clues leading to the result FEBRILE
- Very hot month that’s been linked to anger
- Document about English and British affected by fever
- Winter bug, running a temperature
- Month with bug, sick
- Hot fortnight perhaps on French island?
- Feverish winter month — get cross
- Having broken rib, feel delirious
- Feverish anger
- After brief tussle, the Alsatian is feverish
- Upset after month gets hot
Buddy explains!

The straight part
We know that "sick" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case sick = febrile.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does FEBRILE mean?
FEBRILE adjective- Feverish, or having a high temperature.
- Full of nervous energy.