Hang in there. I had the same type of experience the first time I took out my Koosah. I have some health issues, too and that first trip really took some doing.
Now I'm 4 weeks into ownership. I've built up my strength with daily usage and have made that first 3 miles trip seem whimpy. I average 8 miles a day now...in about 20-30 minutes what with traffic lights and hills. I am building on that and hope to increase my time out on my bent.
I have asthma, too. It is not as severe as yours sounds, but I know that huffing and puffing and coughing can be so frustrating.
Best of luck to you,
Deantha