One of my rabbits, Totoro, had a URI when he was brought to the humane society before I adopted him. I read in his medical history and notes while he was there that they gave him a nebulizer treatment. That definitely worked for him because he started to improve after a week or so, and eventually healed fully. It will take more than 48 hours to determine if the treatment is working. It is important to complete full treatment, especially with antibiotics. Lots of vibes for your bunny.
I would be concerned about the steam treatment because it could make things worse. I know sometimes when people have asthma or colds they find it difficult to breathe in the shower. Your bunny can't really tell you if it's making it difficult for him to breathe.