Steroids are ABSOLUTELY contraindicated in Strongyloidiasis infection.
Steroids not only suppress your immune system response to the parasites but research shows steroids actively induce reproduction causing hyper-infection.
"google" is your friend... you will find nearly every case of fatal strongyloidiasis is caused by administration of endogenous steroid to infected patients. The lung symptoms are an expected side effect of the process. While taking Ivermectin, killing the adults releases larvae, which pass through the lungs. This should pass with continued administration of the drug at the proper dose and the larval count declines with successful treatment. If they would perform "LIVE WET MOUNTS" of your sputum they should find numerous larvae. As well, the new adults undergo a "reproductive burst" in the first couple cycles, in order to re-estblish the population.
I'm assuming you tested positive for the antibody (ELISA?Western Blot) This infection can be very resistant to treatment, particularly in long standing cases with lack of eosinophilic response. Ivermectin may be required for extended periods of time or even indefinitely if the condition fails to resolve. You may achieve further benefit from adding also Albendazole 400 mg twice dailey to your regimen, taken with meals with 40 gram s fat. Ivermectin is also better absorbed with a quantity of alcohol such as vodka. Discontinuation of steriod is absolute must.