Hi Liana,
I think you have a very serious issue here. My thought would be that the wheezing indicates constricted airways and adding that to the rest of the information you provided, asthma is my first guess. If it is asthma, it can be bad enough to kill a cat slowly from weight loss.
Steroids will treat asthma immediately. The problem is that a steroid can make an infection worse. I would strongly recommend that a chest X-ray is taken as soon as possible and to see if the pattern fits asthma. I know there is an expense to this but it it could mean the difference between your cat living and dying.
You could talk to your vet about starting a trial on a steroid but many vets may not want to do this without the diagnostics performed first because if it’s not asthma then the steroid could be harmful.
I hope this helps.
Dr. Clayton Greenway