How old do I have to be to come in and get a piercing on my own, without a parent?

Depends on the piercing. Best to call

And some places require a specific form and it has to be notorized. Just proyecting themselves. Call and ask them what their policy is.

18, anyone under 18 in the state of NY has to have a parent or guardian to get a piercing. And some piercings you have to be a certain age to get in general