I cannot speak to this issue in children, BUT... my 67 year old father FINALLY went to the Doctor TODAY, at my and my mother's insistence he do so, because he has been coughing for almost a month now. No fever. just the coughing. Now he has gone almost hoarse from it. I was literally expecting the doc to say he had walking pneumonia. No. He is having sypmtoms from his GERD (Gastro-esophageal reflux). They are altering his medications a bit, and he also may have some allergy stuff going on (so he's starting to take some Claritin)... but even just sleeping with his pillows propping him up all night LAST night, my mom said he did better. He knew he had GERD before, and takes some medicines, but apparently it wasn't being adequately controlled. Also, my mother and I are thinking he may have been snacking a little closer to bedtime than may be recommended... :)
I would take him to the doctor with a written list of symptoms (and lack of) and as much of a "log" as you can... what time he eats, when do symptoms seem worst, etc. Try to track it very carefully until you can get him in for an appt.
Best wishes to you both.