Is anesthesia always used when setting broken bones?

Sometimes: This will depend upon several factors: severity of the fracture, timing of the injury, patient age and medical condition, coexisting injuries, and so forth. Those mds who specialize in caring for fractures want to assure patient comfort, safety and successful healing. If anesthesia or sedation will be helpful and safe, doctors won't hesitate. Don't worry!

Analgesia: If the broken bone is amenable to a 'closed reduction' then analgesia (pain medication) alone may suffice. If open reduction with internal fixation is required then usually the procedure will require more than analgesia, usually general anesthesia. General anesthesia usually refers to loss of consciousness.

You would prefer it: The setting of broken bones is quite painful. It can be done with a regional block to numb the area, or a sedation anesthetic to render you unconscious while the fracture is reduced. Doing without anything will not be pleasant.