I've got news for you, kiddo. The only law that was broken here, was broken by the tattoo and piercing parlor, who performed work on a minor without the permission of her parents. And maybe by you, in the event that you lied about your age.
Yes, it is 100% legal for your parents to force you to remove them, and to prohibit you from wearing any piercings or tattoos until you are 18 years old.
Here's a law you can show them. It supports your parents, not you.
http://www.statutes.legis.state.tx.u...htm/HS.146.htm