Hopefully one of the MDs on this site will chime in on this, but in my first aid classes, we were told to only use 1 of 2 topical antiseptics on an open wound, either Povidone-iodine or Quaternary ammonium compounds (such as benzethonium chloride, found in Bactine). All such compounds will cause some tissue damaged, but these two have good antiseptic properties and cause little tissue damage if used correctly.
They should be used after cleaning and rinsing the wound. Povidone-iodine is the preferred antiseptic, and can be diluted (to a light pink color) with water and used to flush a wound. Hydrogen peroxide and alcohol cause more significant tissue damage and may delay healing, they should be avoided. Antiseptic ointments should be avoid for deep injuries (more than superficial damage).
These are first aid treatments and do not substitute for proper medical care, particularly if the wound is deep, particularly ragged, contaminated, or any of the symptoms TSandM mentioned develop. As soon as possible consult a doctor for any but completely superficial wounds incurred diving.
Whether either of these will be effective depends on several factors, including the actual organisms involved, the depth and condition of the wound, and the general health of the victim. a MD can assess these after the dive. in the water or in tropical locations subsequent infection should be considered very likely.