Thank you for your query.
Sometimes, a children with recurring cough
presents a medical challenge. I am assuming that your doctors requested chest x-rays and other exams to try and find the cause. The good news is that usually it is not a serious problem, especially if your kid has no other symptoms. I agree with your doctor that the adenoids
are probably not the cause, but may be contributing to a worse sleep. If you can, take him to a pediatrician
specialized in pneumology (lung and chest disorders).
Have a nice day and good luck.