I have A disease called EGPA which has an eosinophilia component but was also on steroids before starting a biologic called Nucala. For me it has worked well. Three shots each month and my symptoms receded. I was able to slowly back off of prednisone by following suggestions from the Mayo site. Slowly, especially as you get under 10 mg is essential to success. It has been two years of shots and I probably may always need them, but worth it to get back to living.
Good luck with your treatment and stay connected to Mayo for the help of good people who have been in your place and are doing well.
MTH13.