First of all.... I am SO SORRY you had to go through such an ordeal. It is never easy for us as parents to see our children ill, so when we feel our child isn't taken care of properly by the medical field we trust so much it's even harder. My youngest had Croup in December and it's definately not a fun thing to watch your child go through.
That being said, none of us can give you the "right" advice as the law is extremely complicated. You may have a case, you very well may not. I can tell you that the cool air WILL open up his airways. The hospital staff can only do so much when they see him per the information they have on hand. And, so much of pediatric care is guesswork since the patient him/herself can't relay exactly how he/she is feeling. I can also tell you that I have never taken my children to the hospital or doctor and had them treated lightly. There are so many lawsuits these days, especially in OBGYNE and Pediatric fields (the two most sued practices in the medical field per stats) that it would be incredibly dumb for them not to take every reasonable measure they could. They may have only done the cool-mist on him BECAUSE he was in another ER and received meds there...they don't want to OVER medicate him.
My BIGGEST advice to you is to go to a lawyer who specializes in medical malpractice. No one will be able to tell you for sure what you should/could/can do but someone who is familiar with the law. No need to work yourself up and get ready for battle in court if you don't even have a case. And, as someone who was blatently fired for being pregnant (I was told my "pregnancy is an issue and you need to find another job") it is EXTREMELY frustrating when you feel so wronged but legally can't do anything about it. It's a hard pill to swallow, but a LAWYER is your best bet. Most lawyers will provide a free review of your case and consultation.
GOOD LUCK and I am, again, SO happy that your child is okay.