I grew worried having swallowed a small insect (6)
I believe the answer is:
earwig
'small insect' is the definition.
(I've seen this in another clue)
'i grew worried having swallowed a' is the wordplay.
'worried' is an anagram indicator.
'having swallowed' means one lot of letters goes inside another.
'i'+'grew'='igrew'
'igrew' with letters rearranged gives 'erwig'.
'erwig' going around 'a' is 'EARWIG'.
(Other definitions for earwig that I've seen before include "An insect, I wager (anag.)" , "Close acquaintance" , "Pincered insect" , "Small insect with aural toupee?" , "Common garden insect" .)