Hi
I feel your concern. Doctors of modern medicine have done their best and we all the doctors strive hard to relieve the patient. In your child's case the best treatment could be Ayurveda which is safe and harmless and doesn't have any side effects or interaction with other drugs of modern science if at all, you have to give concurrently.
Allergens can be anything found around - in atmosphere, in food, in toiletries, in water, milk - anything. Body should be able to resist by natural strong immunity or enhanced immunity. If infection takes place, same is dealt by different measures.
Ayurveda has classical formulae designed for children having Piper longum herb in centre, either independently or in combo with other herbominerals.
These cleanse the brochopulmonary region of allergens,
cough, infections, detoxifies the body etc. Now the dry and productive cough has to be dealt with various combos to be given honey and warm water.
If I were your family doctor, I had advised and insisted to give your child Balchaturbhadra Chooran (a combo of four safe herbs), godnati bhasm and mrigshring bhasm and Sitopaladi choorana in honey and Kantkaryavaleh (in syrup form) for over four to eight weeks to assess the progress. Little turmeric powder may also be added to this combo.
This is safest, harmless, non toxic but little slow to act being natural. Once cured, the allergens and infections will not attack again anytime soon. It enhances resistance against various causes.
For any further query pl feel free to ask through direct question for any help. This medicine is commonly available in India or can be found on net.
Hope its useful for your child too. All the best.