We have many children in our practice who we see for various forms of coughing/wheezing/asthma-type symptoms. Signs and symptoms of respiratory distress are always a concern, and are more of an emergency in babies, of course.
A great way to monitor children with a history of asthma is to use a peak flow meter. Children above the age of 6 should be able to use one fairly accurately, and they are inexpensive and portable. There is some great information here, with a video, on how to use a peak flow meter. Acceptable ranges should be set by your child's physician, based on their height. Once you have that information, you can plug in their height and peak flow reading on this calculator to see if he/she is in the green range. Using a peak flow meter to manage asthma should go hand in hand with an asthma action plan, set up by your child's physician, reviewed yearly, and a copy should be given to your child's school nurse, along with any rescue medications he or she might need at school.
**Just to be clear, this is to be taken as informational only, not as medical advice. I don't know you or your children, and I am not acting as a representative of the medical practice where I work. If your child does have asthma or other respiratory issues, you should contact your child's physician.