The process of healing or recovering is called recuperation. Everyone needs at least a couple of days of recuperation after getting all four wisdom teeth pulled.
Recuperation usually happens after an illness, a medical procedure, or some kind of injury: "His recuperation included keeping his leg elevated for several days." You might even need a little recuperation after exerting yourself: "I didn't expect to need so much recuperation after hiking up that mountain!" The Latin root is recuperare, "get back or regain."