Have you tried instead using a metered dose inhaler that you attach to a aerochamber? It also has a bit of mask, but they only need to breath in and out (normal breathing) for about 10 seconds, while you hold the chamber. And then they are done. It is not strapped around the head. I never used a nebulizer for my daughter as a toddler, as I don't believe it's standard practice in Canada to do so. They will still get their medication in with less side effects.
Inhaled steroids are the mainstay treatment for asthma, and so you should follow your doctor's instruction. These inhalers are very effective in treating asthma and give quality of life to the asthmatic using them.
I have not, what are natural anti-inflammatories? We only use albuterol for exacerbations.
Have you tried using just albuterol and natural anti-inflammatories? Steroids can have nasty side effects. I am managing (after many problems) without them and am doing fine (actually better than I was before).