Crossword Genius

I'm annoyed by wet weather in sheikhdom (7)

Ross

I believe the answer is:

bahrain

I'm a little stuck... Click here to teach me more about this clue!

'sheikhdom' is the definition.
(I've seen this before)

'i'm annoyed by wet weather' is the wordplay.
'i'm annoyed' becomes 'bah' (I can't justify this - if you can you should give a lot more credence to this answer).
'by' says to put letters next to each other.
'wet weather' becomes 'rain' (rain is wet weather).
'bah'+'rain'='BAHRAIN'

'in' is the link.

Can you help me to learn more?

(Other definitions for bahrain that I've seen before include "Gulf region?" , "Arab sheikhdom" , "Arab state" , "kingdom in Middle East" , "Island country in the Persian Gulf" .)

I've seen this clue in The Independent.
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