I suggest inspecting your house for mold. Carefully examine walls bathroom, ceiling for moldy spots. If you find any mold then spray with chlorine or bleach. Find the source of the mold & make repairs. It is usually caused by water damage, leaking roof, damp basement. If the basement is damp, install a dehumidifier.
Is it seasonal? Pollen could be the reason.
Do you have roaches? Roaches & dust mites can trigger asthma.
Also consider this:
One common condition that mimics asthma in infants is bronchiolitis, which is usually caused by a viral infection, most commonly respiratory syncytial virus (RSV).
The infection affects the tiny airways called bronchioles. The airways swell, making breathing difficult. Infants are often affected because their airways are so small that they become easily blocked. For more see this link: http://kidshealth.org/parent/infections/lung/rsv.html