Hi there,
I suffer from asthma. This was a concern for me before I booked my Class 1.
However I was able to pass the Class 1 with the asthma, it was other factors that held me back.
As someone stated above, your asthma should be controlled under medication. I also believe you should not have been hospitalised for it (tho I have to confirm on that).
You have to pass all the 'peak-flow' tests which they will do on you. This is where you blow into this device as hard as you can. If you can pass all that, I think they consider you fit for Class 1 in this regard.
Hope I helped.