Dear che9,
I'm not sure if you son has the same problem as my daughter. Few weeks ago my daughter coughed when she woke up (but not very serious). But we could hear the 痰 stuck in her throat and it took some effort for her to 'swallow' the 痰. Sometimes she looked as if she was going to suffocate by the 痰! We took her to a doctor but the medicine did not help. She ate some 猴棗散 and it helped a little bit.
Later another doctor told me tried to give her a few drops of salt water (生理性鹽水) to her nasals (nose,鼻孔) using a 膠唧筒. The doctor said that this salt water (9%) was sold in the Chemist. He gave me two little bottles of 生理性鹽水.
The doctor explained to me that the 痰 was caused by 分泌物 from the 鼻 and bb's narrow nasal passages. If we can clean the nasal passage more often, then the 分泌物 from the 鼻 will be diluted and will not become 痰 (杰杰的 分泌物) sticking to the throat. I then gave her a drop or 2 of salt solution before feeding her and now she has no more coughing.
At first I was afraid that the 鹽水 would choke her or make her uncomfortable, but no! Besides the funny look on her face when I gave her the 鹽水 drops, she was alright. If possible please consult your doctor. Hope it'll help.