I appreciate this can be a nerve wracking time for couples, and may not have been your first option for your delivery.
Anaesthesia for caesarean delivery is very safe, and is designed to ensure you (and your partner) enjoy the birth of your baby and are comfortable during the procedure and in the post natal period.
Caesars are performed under a spinal block, which involves a small amount of long acting local anaesthetic and opiate based pain relief placed in the spinal fluid via a very fine needle. This differs slightly from an epidural, in which case a small catheter is left behind through which we can infuse/inject subsequent doses of local anaesthetic. Epidurals are placed for pain relief in labour; if you require caesarean delivery after having a labour epidural we usually elect to top this up with local anaesthetic.
There are very few risks of spinal anaesthetic. Despite enduring myths, neither spinals nor epidurals are associated with back pain long term, and the risk of nerve damage is incredibly small.