Piece of peach oozing might make you sneeze (5)

I believe the answer is:

achoo

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'you sneeze' is the definition.
'achoo' can be an answer for 'sneeze' (I've seen this in another clue). I am not certain of the 'you' bit.

'piece of peach oozing might' is the wordplay.
'piece of' says the answer is hidden in the clue.
'ACHOO' can be found hidden inside 'peach oozing might'.

'make' is the link.

Can you help me to learn more?

I've seen this clue in The Irish Times.

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