Grounding, no matter how long, is usually not very effective and is sometimes very hard to enforce. First, I suggest you sit down with your daughter and state very firmly what your feelings are about her betrayal of your trust. Don't talk about the reasons you didn't want her to get her nose pierced. Next, impose some or all of these consequences, which might be somewhat more logical and natural. Say something like, "Because of the choices you made to disobey and lie to us, we, as parents, also have to make some choices about your behavior in our home. You will have to build back the trust you lost. You may not go to ... for a month. "(If she used a certain place or friend as her excuse to get out to do the piercing, mention this place or person.)
You can also say: "Although we cannot control what you do outside our home, we do set the rules in our home and you may not wear the nose stud when you're here or when you're with us." Be very firm on this. Don't let her sit down with the family for dinner unless she has removed the stud.
Keep focused on consequences for her making the choice not to follow your rules. Don't think of it as punishment. You don't need revenge -- you need to be able to trust her as part of your family. It's her responsibility now to rebuild that trust.