Thanks Ethan again for your reply. Here are some things I think you might want to explore with your doctor. There are two conditions that comes to mind that might be affecting your son: Cyclic Vomiting Syndrome & Epilepsy cluster of seizures. From my experience during my neurology clinical, your son may be suffering from a form of Epilepsy that manifests itself as these vomiting spells. Epilepsy is like a cluster of seizure episodes throughout a year, and you end up having more seizure episodes each year as opposed to one isolated seizure and not have any for years or ever again.
The fact that your son has been vomiting so many times over the past months without reflief from anti-vomit/ememics medications is an indication to investigate the cauase of his vomiting spells deeper than just from his stomach. A neurologist would have to order an EEG (electroencephalogram, "encephalo"~ brain), which is like an ECG (electrocardiogram) for your heart, but for your brain. It measures the brain's activity via electric brain waves. II his case, his neurologist may want to do this EEG at night while your son sleeps to record how it functions and particularly how the brain functions when his vomiting spells happen. If the brain waves record abnormally during his vomiting spells, then it will reflect a seizure during that time.
If no seizure is recorded during his vomiting spells, then my second thought would be CVS or cyclic vomiting syndrome. Outside of those two, vomiting in a child could arise from congenital malformations in the abdominal organs, such as what's seen in intussusception (with bloody/mucous stools, a current-jelly like appearance),others that are usually noticed at or near birth like pyloric stenosis & TE fistulas. Since you said that the only significant problem after birth was sleep apnea, his vomiting may be more in nature of the first two conditions I mentioned.
Therefore, check with his doctor to investigate CVS or Epilepsy possibilities for your son since he is still vomiting and meds are not resolving it. Is there anything abnormal about the appearance of his stomach/abdomen area, such as any thing protruding out or if his tummy is tight or distended? Have his pediatrician double check for those things. However, since your son has had such a long history of vomiting, make sure that his electrolytes,fluids, & blood pH are balanced. If he is ill-appearing/irritable/changes his normal child behavior/listless/headaches/stomach pain/blood in stool/vomit/urine, fever, problems breathing or inside his mouth is dry or diarrhea, take him to the ER to be evaluated.
I will give you links to review these situations in more detail, and again review the above possibilities with your son's pediatrician. I hope this information will help you and your son on his quest for health and wellness. I empathize with your son's plight and I hope your family will finally be able to have some options to work with. Please feel free to contact me for additional help. Thanks for posting your question and best of luck! :) ~RoseMD