Do you mean that it appears your child is having trouble breathing yet he is still running around all day?  If that's your question, it's quite common.  I see it all the time.  In fact, it happens with my child when she has asthma. Children don't use their asthma as an excuse.  It's normal for them to keep active even while they appear to be sick.

I would say that if he has asthma medicine I'd give it to him as recommended by his pediatrician, yet if he's active I wouldn't restrict his activity.  If he's running around that means he's well enough for activity.  Plus activity is good for asthmatics anyway.  Just be wary of the signs and symptoms of worsening asthma (click here and here and here), follow his asthma management plan, and keep in touch with his pediatritian. 

I know, it's hard not to "panic" when your child looks sick, yet it might just be the best action. 

Rick