Call him tomorrow. We have no way of knowing when you'll the medication will have done it's job. I do suggest that it will take time and you've only been on the new medication for a day. Always call when you have concerns. That's why he gets the big bucks.
My granddaughter has asthma which is made worse by a virus. The doctor does sometimes give her an oral steroid. I'm not familiar with what you mean by a combo steroid. Perhaps it works as well as an oral one. Since you expected to get an oral steroid, I'd ask the doctor why he's concerned about the side effects this time.
I'm also do not know what LABA is. I could not find it on the Internet. Perhaps the doctor has given you which he expects to work as well as an oral steroid.
Do not change doctors. Doctor shopping just lengthens your treatment time. This doctor has your records and has begun treatment. A new doctor would be starting over. There is no one magic treatment, after all. If you want an oral steroid be assertive with the doctor and find out more about why he made this decision.