I have pain in my left butt that prevent me from sleep at night. I want to make the cortisone injection but I am afraid since I have fibromyalgia also.?

Steroids and FM. Targeted steroid injection for an isolated non-fibromyalgia problem shouldn't cause any problems. Steroids don't worsen fibromyalgia.
The injection might. Help and it should not negatively impact your fibromyalgia.