Fussy and irritable, looking neither to right nor (later) left (5)

I believe the answer is:

picky

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'fussy' is the definition.
(I know that fussy can be written as picky)

I don't understand how the rest of the clue works.

Can you help me to learn more?

(Other definitions for picky that I've seen before include "Discriminating" , "Excessively fastidious" , "Choosy" , "Excessively particular" , "Finicky" .)

I've seen this clue in The Times.

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