Could be...
1. Pertussis, especially if your son is throwing up due to violent, and I mean really violent coughing. Oftern pertussis has a cough unlike what most people have seen, and it is sometimes frightening to witness. Since many children nowadays are not vaccinated, pertussis is actually more widespread than we all think, and your pediatrician may not be able to recognize it right away (the younger docs may have never seen the disease, and the older docs may have forgotten what it looks like). There is testing available. This is definitely the first thing I would think about.
2. RSV...it can leave a cough that lingers for up to a month, although not as violent as pertussis, but with occasional vomiting after coughing.
3. Middle ear fluid...there are cough receptors in the middle ear that can be tickled by the presence of fluid.
4. Asthma...not all asthma wheezes, sometimes it coughs.
5. Allergies...this time of the year, mold and (I think) ragweed are most common. There is testing available as well.
Unfortunately, for 2 and 3 there is not much to do except wait it out. For pertussis, there is an option to treat with Zithromax, however, after the first 3 weeks of illness the effectiveness of treatment wanes. Of course, for asthma, the best way to determine this is to simply treat with albuterol and see if it works. Allergies can also be treated easily with a nasal spray or Singulair.
No matter what - avoid cough and cold preparations at all costs. These can harm your child, and most of the time they either do not work or work only a little bit.
I would go back to your doctor and present these options. If you are not satisfied, do not hesitate to get a 2nd opinion or request a referal to a pulmonologist (lung specialist).