Hi BrianG – Jimmy's right, but try to keep resolution of your problem at the local level, as in my experience the formal mediation conducted by the NSW Office of Fair Trading is often superficial; all very frustrating!
Balcony drains are typically under-sized, and this combined with the grate at the opening often results in blockages — I'll bet that dirt and debris from your neighbour's pot plants has caused a blockage.
In any case and as Jimmy has said, any Strata Manager who's worth what you're Plan's paying them should be able to facilitate resolution of the problem.