I'm not even a beginner, but I'm doing my best to become one. I live in Poland and I have no access to classes, so I'll try to learn online or buy a self-teaching book. The word in the topic is my job, or one of my jobs. Could you please include the pronunciation as well?

The answer is at http://www.focal.ie/Search.aspx?term=psychologist , but this is totally the wrong way to approach learning a language. You do not start by learning "psychologist" as your first word. Try "hello" instead. How do you plan to use the word síceolaí if you have not learned any verbs, pronouns, or even the definite article. You asked for the pronunciation, but until you have studied the sound system of Irish you won't be in a position to enunciate the words.

sikioły, with ł as in the former standard pronunciation or as in Russian.

sikioły - I am not sure about that. Síceolaí has three long vowels, but the Polish transcription you gave doesn't appear to have any long vowels.

IPA: /ʃi:'kʲo:l̪ˠi:/

That's true, but that's the closest you can get without getting into explanation of technical details.