Hey TM, I'm sorry that Duckie is so sick.
We have had a nebulizer at home for years, in fact, we're on our third one - it is a Godsend to have that nearby and with 2-3 treatments daily, the symptoms really do improve faster than waiting for the other medications to kick in and using an inhaler. An emergency inhaler should really only be used for that - an emergency. With the neb, you will be able to schedule her treatments and maintain and even level breathing capacity and improvements.
Cephaclor (sp?) was always the best treatment for both my girls when they were younger and had asthmatic bronchitis. It just worked like magic and improvements were usually seen by day 2, along with the neb when needed. They rarely needed pred, but I was always on pred as a kid and into adulthood. I hate pred, but realize that it is necessary at times.
Sending healing thoughts that Duckie improves onces she's on the right stuff! I am currently battling a chest infection myself and have been nebulizing twice daily. Today is an improvement over yesterday. Best of luck - hope you're able to catch up on your sleep too.