The copyright in the photo is owned by the person who took the photo unless it has been explicitly assigned to someone else. I assume that person is you.
The copyright of the tattoo design itself is another matter and you may not be allowed to reproduce a similar design if you don't own the copyright and the artist does. My understanding, though, is that most designs are copied out of books which presumably either feature rights-free designs or come with a license to use the designs they contain.
But this is not really a question of "copyright", it's a question of "false advertising", i.e. by posting those images on Facebook on a given date, are you "advertising" the fact that a reader could get a similar tattoo done by the same artist at your studio in the future?
Without seeing it I would say that you are probably NOT "advertising" that fact and that you're OK - unless you're somehow explicity stating or implying that fact under the photo, of course. It sounds to me that your Facebook posts are more akin to journalistic records than advertisements.
By the way, I am not a lawyer but do have some experience in copyright, trademark and patent law and social media ... I suspect more than your ex-tattoo artist. If things get pushed any further, though, then you will need to seek proper legal advice if you want to fight it. Until that, I'd just ignore it ...