Yes. Almost all of the tattoos sold on Co:Create are unique. That means the artist will not resell this tattoo to someone else.
You can confirm whether your tattoo is unique, or part of a collection, in the "Design Details" section of the tattoo's information page. Below is an example of a unique tattoo, because it is listed as a 1 of 1.
Tattoos that are part of a series of three, for example, will be listed as 1 of 3.