Damaged wire while drilling wall caused power to go out. How to fix it properly?
So it sounds like the AFCI breaker did its job and saved you from a potentially nasty jolt. The AFCI detects the arc (i.e. your metal drill bit contacting the live wire) and cuts the power.

If the wire wasn't severed, you can probably get away with just wrapping the wire in electrical tape and then wrapping the whole scar. If the wires were severed, you can use an inline splice to reattach them without a box.