One of my grand daughter's was born with GERD. My son and his wife were up with her colic and reflux for many nights. She was given simethicone and needed her tummy rubbed every so often to help her with her problem. Sometimes it made her vomit.... So sorry you suffered the loss of your little one. - My grand daughter, however, did not have cyanosis. Her oxygen was good.
When the did the otopsy they had said that it was acute pneumonia. He had fluid in his lungs. When I took him in the er it was BC of him having the bluish color an wasn't eating well. Not only that he was 4 weeks early in delivery. They had him on oxygen on the way to the hospital an he seemed perfect when on it. The Dr in the hospital took him off an when his number on the counter when down to pretty much zero they said the counter didn't really work. But you can tell he wasnt being well as a new mom I believed what the Drs were saying. They didn't run any kind of test on him or anything an just assumed an sent him home
Firstly, I'm terribly sorry to hear about your loss. It is always heard breaking to hear about a death of such a young neonate.
With regards to your questions, bluish skin tone is known as cyanosis, which is caused by a lack of oxygenated blood to the specific area. In your case, Central Cyanosis (Cyanosis of Centralized Systems like mouth, tongue or the core of the body) can be caused by many issues, generally relating to the Central Nervous System, Respiratory System, Cardiac Disorders, Blood Disorders and/or other issues (Altitude, Hypothermia, Obstructive Sleep Apnea).
Also, Blue Baby Syndrome which can cause central cyanosis are generally caused by cardiac defects.
The only way to know the true cause of death is to have a postmortem performed, and even then it may or may not be due to the reasons you brought your child into the emergency department.
I wish you all the best in grieving your terrible loss,
--Phil