Cigarette odor on clothes and an asthmatic child, what should I do?

Quit? The most proper action is to quit smoking or eliminate the child's exposure to this trigger.
Avoidance. Although trace tobacco smoke chemicals on a persons clothing might trigger allergic-type symptoms, this situation would be unlikely to trigger a severe asthma attack. Of more concern is a higher level of passive tobacco smoke exposure in a contained environment over a prolonged peroid of time.