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I would ask the advice of your PS. Generally if the wound has healed then one can start doing what one normally does. A chlorinated pool however may not be in your best interest and you should ask your PS.
Though I can't specifically answer your question since you are not my patient, if a surgery site is still red and irritated, chlorine will only inflame it more. It is best to have the physician who performed the surgery examine your nose and make that decision.