The most common and most likely answer to this crossword clue is the 12 letter word DESENSITIZED
I've seen this crossword clue in The Guardian
D
E
S
E
N
S
I
T
I
Z
E
D
Buddy explains!
The straight part
We know that "could antihistamines make one this" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case could antihistamines make one this = desensitized.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.
Crossword Answer definitions
DESENSITIZED verb- To cause to become less sensitive or insensitive.