If your children are experiencing coughing even with their inhaler, it may be helpful to try an antihistamine like Claritin or Aerius. This could potentially help reduce congestion and mucus production causing the cough. It is recommended to give it a try for 5 to 7 days and if there is no improvement, it would be best to consult a doctor. Keep up with nasal hygiene and continue using their inhalers as prescribed.