unfortunately you are right about the long waits at the Public hospital...i waited 3 hours just to get my son admitted for jaundice, but they are very thorough and the wait is really worth it. my son is still at QMH but not for jaundice any more but a bacterial infection that they detected only from a slight fever, which would have probably gone un-noticed elsewhere. so, wait is long, but well worth it in the long run.
but since you have gotten so many opinions, i think your baby is OK - heart breaking as it is, you will probably just have to wait it out and do things that your baby enjoys or makes him comfortable....taking a bath perhaps so there is more exposure to humidity and the cough is not quite so bad?!? hope you LO feels better soon.