Is it absolutely necessary to have an epidural injection for inflammation or can time un-pinch a nerve?

Time is the biggest: Healer with 90% of disc herniations getting better without surgery. Epidural steroid injections are options to help with pain control while your body heals-they are not mandatory.

Not absolutely : There are a few treatments that "absolutely necessary" such as life-saving or organ-saving ones. If epidural streriod injection was rightfully indicated it may expedite recovery.