Are over-the-counter remedies good for the control of catarrh in children with asthma?

No: Catarrh (meaning inflammation and thick discharge) in children with asthma may be part of the normal asthmatic process, and should be treated with preventative, anti-inflammatory controller medications if it occurs frequently or persistently. These are only available by rx in the us. It also often can be from a secondary infection-sinusitis or bronchitis and may need treatment with a antibiotic.

Maybe: You can always start with over the counter medicines. If they work - great, but if they don't make sure you contact your child's doctor in order to prevent an asthma exacerbation.