I don't quite know what you're asking ... but these are correct sentences in English with almost the same meaning:
I am not an artist. (This is a normal sentence but pronounced very clearly, or stressed.)
I'm not an artist. (This is a normal sentence with normal pronunciation.)
I am no artist. (This sounds defensive.)
I'm no artist. (This sounds defensive.)
You cannot just say "not artist". We need an article in English: an.
No particular reason - this is just another sentence with a slightly different meaning. 'Nem művész vagyok.' says it's not an artist what I am (but I am something else nevertheless). 'Nem vagyok művész.' says I'm not [certainly] an artist (and no further hint is given if I am something else at all).