Notwithstanding the issues of your neighbour not being an Owner and whether the ducted air conditioning system serving your Lot is yours or common property, you have done everything that can reasonably be expected of you in order to check that the external component of that system is operating correctly, and whilst it’s not clear what the ceiling of your neighbour’s Lot has to do with the matter, your “right” is to ask her to raise all of her concerns with the Strata Manager who’s paid (by both of you) to investigate and to recommend any necessary actions to the Owners Corporation.