Hi. I have chronic asthma & my kids definately have it whenever sickness or allergies come about. Our pediatrician has prescribed us albuterol for the nebulizer (so that we always have it available) & when it runs low, he refills it. Also, the prednisone prescribed is good longer than the experation date (I forget if it is a year or two years, ask the doctor)...he prescribes more than the needed five days so that we can start it right away if one of our little ones develope the wheezing/coughing. You need to keep up with their weight to make sure of the correct dosage. I'd ask you doctor about having some prescribed to keep at your house so that you can start it straight away, then have them be seen if needed.
Otherwise, the nebulizer should treat the asthma symptoms. You can use the machine treatment every two hours if needed if breathing is really labored (like they do in the hospital) BUT, it is recommeded every 4-6.
I'm not sure how old your little one is, but this is what we're doing for my almost 20mo. old, almost 4yr old, and almost 7 yr. old. We've delt with this since my oldest was 3 months old & developed RSV/bronchiolitis...we're just always going to deal with asthma issues. The trick is to catch it before it becomes more serious. My littlest guy ended up having pneumonia last March because we waited a little too long.
So, yes, I'd talk with your ped. about the different options & steps that he'd like you to take so that you can avoid this in the future. Hope that this helps...