Although each of your sentences share the same first person subject, they each have subtly different implications.
- This article is about me, a programmer.
Here, you identify as a programmer, but there may be other aspects of you and your life the reader will learn about.
- This article is about me, the programmer.
Colloquially, "*me, the X" suggests a focus on a particular aspect of yourself and your life. I expect the article to be biographical and perhaps even confessional. It suggests that everything in this article will somehow relate to you being a programmer and/or will be expressed from your mindset as one.
Regarding your similar sentences, we generally say "... the X in me" when referring to a specific aspect of ourselves. If you say, "... a programmer in me," it sounds odd, as if there are several programmers in you (or anywhere), and you are referring to a particular one inside of you.
Finally, for your titles, I would suggest using I instead of Me, and for the same reason, would avoid the article 'a' and stick with 'the' or no article. I don't know of any "rules" about this, but once you follow the pronoun with a comma and "the X", it sounds more natural to me for the X to be in subject form.
Both these titles sound like biographies or confessionals:
I, the Programmer
This sounds like you will be describing your work as the sole programmer in the story. Other people may have been involved (design, distribution, etc.) but you alone were the programmer.
This one sounds like a nod to Isaac Asimov, who ironically objected to that title (he had wanted to title the collection Mind and Iron) as it had already been used by another author. (Plus, I, Robot was not even told from the perspective of the robot!) My familiarity with I, Robot would color my expectations of this article. I would assume it would be biographical and told from the perspective of someone who approaches life and work with computer-like precision, but who nevertheless wants to be recognized for his/her humanity.