Does Polish perhaps make a distinction between a 'job' (which is something you do to earn money, and can be either a part of your profession or something temporary) and a 'profession' (what you've been trained to do, usually over an extended period of time at some school, and what you plan on doing for a long time, even if you go to a different company or location)m
Profession is "zawód". Which is accidentally also a possible translation of "disappointment".
Oh wait, it's actually a sentence with "zawód"... well, it may denote what you do for a living, but you can treat it more like "profession" as well. The closest thing to what you mean could probably be "wykształcenie" (one's education): "Z wykształcenia jestem historykiem" = I am a historian by education.
To jest mój zawód/ To jest mój fach - It is my profession/ It is my trade (profession)
A profession is not a job. It is an education and set of skills (wyuczony zawód) which allow you to work in a certain specialty.
If you are employed or you have a job, you have an occupation (wykonywany zawód, praca) which may differ from your profession.
"moich" is completely wrong here, I'm afraid. Not only it's the wrong case (either Genitive, Locative or Accusative), it's also wrong grammatical number (it's plural).
This is a simple "This is Y" sentence, with Y in Nominative. "zawód" is a masculine noun. The right form is "mój".