This should've probably been included in the vanilla version of the game, but it wasn't, so mods have done the job.
Looks Mirror adds a new item for your settlement: A mirror. Not just any old mirror though. This mirror can be used to change your character's appearance at any point.
Simply walk up to it and you'll be able to edit how you see fit. This is a necessary addition to most settlements, yours included.
This article may contain affiliate links. Click here for more details.
Give it a shot.