What you're describing sounds like coccydynia, pain in the tailbone, which is a common after effect of childbirth rather than something caused by the anesthesia. It usually comes from pressure or a small injury to the tailbone during delivery and can take months to settle on its own.
Next Steps
Try a doughnut shaped cushion when sitting, avoid sitting fully upright on hard surfaces, and use warm compresses. If this doesn't improve over the next month, see your gynaecologist or an orthopaedist, who can check if you need imaging or physiotherapy.
Health Tips
Get it checked sooner if the pain worsens, spreads down your legs, or you notice numbness, since that would need a different workup.