What is the analgesic stick used after surgery? Why does it stop hurting? What is the principle?

An analgesic pump, not an analgesic stick.

The analgesic pump is just a medical device, and it is the medication that is added to it that makes it work. It is usually an analgesic or local anesthetic that is pumped at a certain rate to achieve a stable analgesic effect.

Different routes of administration of the analgesic pump, the method of administration and principle are different. For example, an epidural analgesic pump is basically painless after use.