The wheezing, and the cough to the point of vomiting, would be my cut-off point. As a mom to an asthmatic, the wheeze is not something to mess with. Having said that- is he wheezing or does he have raspy breathing? If you have seen an asthma attack, you will know the difference.
Not sure how long he has been in care, but when a child first starts daycare (or school, etc) they contract 7-10 viruses in the first year, on average. Given that a virus will last between 5 and 14 days, it seems like they are ALWAYS sick. This should get better as the immune system strengthens.