I highly recommend checking out this website: http://www.fritzthebrave.com/
especially the part about inhaled meds. There is a device called an AeroKat
that allows bronchodilators such as Albuterol to be used on felines, which would be much more effective in an emergency than having to wait for the pills to kick in. The other problem with oral or injected steroids is the increased possibility of developing diabetes. Using an inhaler eliminates that risk. I would talk to your vet about an AeroKat as soon as possible, or find another vet if they aren't willing to explore that option.
I wish you all the best! Asthma can be incredibly frustrating.