Unfortunately side effects cannot be predicted.
If you so much as think or anticipate some undesirable side effects, you probably should be somehow monitored till you feel safe. It need not be an in the hospital thing, unless preferred, as perhaps a good friend could be your monitor.
I also have asthma and have anxiety problems. It is truth that the asthma medication makes me more anxious but I'm taking them. Maybe you should try the steroids and sigulair for 1 month and see how you feel, so you can decide whether you want to continue with them or not. everybody has different side effect to these meds so unless you try them you won't know if they are good for you or not.
If the doctor ask me to take oral steroids for long time I would definitely be afraid but inhaled steroids are not as bad, they go directly to your lungs. I do have a side effect from the inhaled steroids, my voice is a little rough sometimes. I also tried singulair for a month but it didn't make any difference on my asthma so I stopped it.
hopefully this help!