Character suddenly has wrinkles

Maybe...did you change any video settings.  It has been awhile but I thought it was related to video settings and things "there" but not drawn because of lower video quality, and then with update, they are drawn because the settings were tweaked some.  You may could just lower the settings some and get rid of them, otherwise, unless you could find a save editor to modify the face data, you would have to restart.  Waking up from rift closing??  Are you talking the first major rift where you wake up in bed when the Elf disturbs you??  If so that is barely started the game, and easy restart.  Even the second Major rift close just before Skyhold isn't horrible, at maybe 1/3 the way through game.

Also, if you've downloaded and installed the Black Emporium, you can change your characters face using the mirror there. 🙂 Just be aware that certain types of mods will cause issues there, so best to turn off any cosmetic (such as face or hair textures) mods before you go there.

Lol, you know, I always forget about the mirror in the Black emporium, I never use it and just forget it is there.....

Good suggestion.

Make sure the shader setting is set to high or ultra. If it's too low, the scar textures are replaced by wrinkly textures.

Shader quality used to be bundled with mesh quality, but they separated it in a patch. There was an unofficial fix for that before, so if you ever applied that, you have to remove it.