Wow! Shades of our family's past! Our now 12-year-old used to get asthma whenever he got a cold...and he got colds A LOT. He never got to the point of hospitalization, but we nebulized him many, many times. And one time he went to pneumonia, but we were able to care for him at home. It wasn't extreme.
A few questions for you. Does he have any indication of asthma when he doesn't have a cold? Does he get eczema easily? Is he in full-time daycare? What size is the daycare?
Our son got sick frequently when he was little, but we never had him on his nebulizer all the time. It was only when he got sick and he seemed to be wheezing. We used albuterol. (I'm not familiar with Pulmicort or Orapred.) The albuterol would occasionally jazz him up but not always. More often than not, it just helped him breathe better. The effect was amazingly immediate. When he was out of the woods, though, we did not nebulize him. We just used it episodically.
Every child's level of asthma is unique, but if your son just tends to get it when he gets a cold, he may be a good candidate for growing out of it as he grows older. As their wind passages get larger, some kids grow out of the tendency towards asthma. Fortunately, our son grew out of it. I hope your son is that lucky as well. (Even my niece, who was 3 months premature and had asthma pretty consistently when she was young, has grown out of it as an adult. But that's not the case for all situations like that.)
You may not have this option, and our doctor may have been a little old-fashioned, but he recommended that one of us go part-time if we could swing it, so that our son wasn't in childcare so much. I have to admit that that change made a huge difference. With our son not in the germ soup on a daily basis, he got sick much less often. We switched to just 2-3 days a week, with me home the rest of the time, and he faired much better. Like I said, you or your husband may not have that flexibility, but it might be something to think about.
One other thing...are you sure it is the medicine that is making your son vomit? The reason I ask is that our son rarely vomited but it was usually when he was really mucousy. I think he just would gag on the mucous and that led to his vomiting. We deduced this because most of what he vomited was mucous.
I also ask about the eczema because our son had it A LOT when he was little. Sometimes his skin would get so raw. We used Aquaphor (sp?) for years, and occasionally we used hydrocortisone when it was really bad. But the thing we found later that worked wonders was Hydrophilic Ointment. It wasn't a prescription drug, but it was behind the counter at our pharmacy. You had to specifically ask for it. It had a Noxema consistency and feel to it, and it worked great on our son. Once we started using this new product, we rarely needed to use hydrocortisone.
We never really were able to peg what would set off our son with the eczema, so we tended to just address it when it appeared. But I suspect it is some sort of allergy.
Years later, our son became notorious for getting nosebleeds. My husband and I used to get them a lot when we were young as well. Our son's doctor suggested that it might be allergies and he put him on Flonase (or a generic version of it), which I also use. It seemed to really help him for a while. He is no longer using it, but it seemed to do the trick while he was using it.
Back to work and daycares...the daycare our son originally was at was pretty large. It was a great facility but it probably had 40-50 kids spread out over several classrooms. The germ pool was profuse. Later, we found a smaller daycare with just about 15-20 kids and only 7 kids in his particular class. Whether he was just getting older, or the class size reduction was the trick, he seemed to get sick much less often. If your son is going to a daycare that is large, it might be worth it to explore what other options you might find in your area. It could possibly make the difference.
I hope some of this helps. It's hard seeing your little one get sick and have a hard time breathing. Best of luck and happy holidays!