The most common and most likely answer to this crossword clue is the 3 plus 4 letter word ICE PACK
I've seen this crossword clue in Financial Times
I
C
E
P
A
C
K
More clues leading to the result ICE PACK
Buddy explains!

The straight part
We know that "Maybe swelling number" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case maybe swelling number = ice pack.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.