Did this vet take a culture and send it to a lab to determine exactly what microbe is causing the infection, and what medication will be effective in treating it? Baytril is just a broad-spectrum Antibiotic, that's it. It treats only bacterial infections, and not even close to all the possible bacterial infections that could be causing his infection, let alone if it's being caused by a fungal infection... Or did they do an x-ray?
As Tracie said, Tylosine/Tylan 50 is the best drug to use in a nebulizer for an Upper Respiratory Infection, I've been using this for my parrots several times and once for my Dragon, and doing a 10-15 treatment once a day for a week clears them very well...The advantage in the US is that Tylosin/Tylan 50 is available here over the counter at stores like Tractor Supply, it's sold for farmers to be able to treat their livestock...Do you have any stores in Canada like Tractor Supply, where you can just walk in and buy different antibiotics, anti-fungals, etc. for farm animals, dogs, cats, etc.? If so that's your best bet, if not you may be able to order it online somewhere, or ask you vet to call-in a prescription for it, that way the pharmacist could compound it correctly for you, although when you nebulize it instead of giving it to them orally the "dosage" doesn't have to be as exact...
Tylan is the brand name for Tylosin, and it comes in different dosages, Tylan 50 is the weakest, that's what you want, no need for Tylan 100.
You can make you own nebulizer pretty easily...All you need is a plastic tub that is around 50-55 liters with a lid, and then you can actually use one of the vaporizers that is sold for humans. I bought one at Walmart for $20 that came with a mask meant for humans...Then I just put the vaporizer inside the tub, poked some ventilation holes in the lid of the plastic tub for ventilation, and then you just dilute the Tylosin/Tylan 50 with sterile water/distilled water and put it in the vaporizer chamber. Using a small, personal vaporizer this way eliminates the need for putting hoses from the nebulizer through the lid of the plastic tub and then having to use duct tape to tape-up the gaps in the lid around the hose, etc. Then I just put the parrot/beardie in the plastic tub, turn on the vaporizer, and shut the lid. You'll see the steam/medicine venting through the holes into the air as well as filling the tub, but you don't want the tub to be so cloudy that you can't see your Dragon, you might have to experiment a little with the number/size of the vent holes in the lid, as you don't want too much of the medicine escaping the tub, but you don't want to totally "Fog" your Dragon. Then you just let them in the tub to breath-in the medication, directly into their lungs and the source of the infection, until the entire dose vaporizes and the vaporizer is empty and stops producing any fog...Do that once a day for week and it typically works very, very well...
You might also ask your Exotics Vet if he actually has a Nebulizer Chamber in his office, a lot of Vets use this for both birds and reptiles, and they have them in-house. But you don't want him to use Baytril, that's not going to do it.