My rescue is 99% macaws and I've had this same problem with a few of them. Interestingly, macaws have the highest incidents of allergies than any other psittacine; if not any other bird.
Let me review a few of the causation's I see more of: Rhinitis (inflammation of the nares/nostrils). There would likely be a nasal discharge involved that may be clear, cloudy or yellowish; thick or thin. The underlying cause may be anything from viral to bacterial or fungal.
It could also be a reaction to a foreign object, which could be as common as dust or other bird’s feathers/dander.
Our blue & gold macaw (Sadie) has this condition flare up twice a year during high pollen counts. It’s especially common in macaws and amazons (birds from rainforest/tropical climates). The discharge may harden (rhinoliths) and if not (gently) wiped away regularly, it may plug the nares and cause several other severely complicated health issues.
Use a soft, warm, moist cloth to gently wipe the nares clear.
Another possibility is infection of the air sacs (air sacculitis). Symptoms for this includes coughing, wheezing and labored breathing. It’s often more noticeable after the bird does something strenuous (like a flight). Treatment would depend on the infection (fungal, bacterial or viral).
I commend you for doing the right thing with the vet visit. I must ask though if this is an avian only vet. There are a couple of things I find perplexing in their suggestions, but they had the opportunity of a full hands on visit and exam so it may make more sense.
If your bird is having normal droppings, is not fluffing, losing balance or sitting at the bottom of the cage, and is eating/drinking normally, it is probably not an emergency; however, if along with respiratory problems you notice the bird fluffing and preferring to be at the bottom of the cage – or even in one area of the cage, not moving much on their perch – this is an urgent care situation.
In the meantime, as well as keeping the (nostrils) clear, when it comes to birds from tropical rainforests like macaws, amazons try installing a vaporizer (as opposed to a humidifier) in the room. The hot steamy air can be helpful to both feather quality and respiratory tracts. Vacuuming instead of just sweeping or dusting, needs to be done daily. It might sound like a lot of work, but when done on a regular basis it’s really not so bad. I do it twice a day to help one of the permanent residents, a wonderful macaw with acute allergies. She’s improved quite noticeably with these efforts.
I think there’s a great deal of valuable information here
Further, removal of carpet might be considered - there's something to be said for beautiful hardwood or tiled floors in ease of care - and room sized area rugs are far easier to maintain as opposed to shampooing wall to wall carpet every 3 months to help your bird avoid dust and dander.
Daily cage cleaning of course - tedious but extremely effective.
Most of the macaws in my rescue come from neglectful, hoarding or outright physical abuse situations that can be devastating. One is permanently, totally blind and crippled from his sadistic owners and yet he's the sweetest, most loving bird I've ever known. Another is our 'allergic to everything' girl who hasn't had a single bout of allergies since I made the changes suggested to you here. Well worth the effort I promise - poor thing was miserable when she couldn't breathe.
I'm here for you all through this - so let me know how you're doing ok?
And thank you for rescuing this lucky guy
You won't believe how it will change your life