I too have asthma aussie (COPD actually) and have to use oxygen occasionally - I know all about that. That is where a severe allergy goes. BUT I adopted a cat - will she hurt my health. Not likely! More than likley, she helps me - and my patients! With her antics, her cuteness in a bleak day. There are many steps one can take to reduce dander and to to over ome allergies.
I was not being critical of you nor of them personally but one of the top reasons people bring in pets to shelters is allergies so people are a little questioning about that excuse now. I know it is extreme but many SPCA's kill pets in a short period of time. (There are some notable exceptions).
I hope the cat finds a home.