Fialkowska began to study piano at the age of four with her mother and in 1960 enrolled in the École Vincent-d'Indy in Montreal. In 1963, at the age of 12, she made her debut as a soloist with the Montreal Symphony Orchestra and began studying with Yvonne Hubert. She pursued her secondary education at the Montreal girls school The Study, graduating in 1967. The following year, at the age of 17, she simultaneously obtained undergraduate (Baccalauréat) and Maitrise from the Université de Montréal. During this period, she also studied in Paris with virtuoso and teacher Yvonne Lefébure (1966, 1968–1969). In 1969 she was awarded 1st Prize in the CBC National Radio Competition for Young Performers in Canada and travelled occasionally to New York City for private studies with Sasha Gorodnitzki. In 1970, she settled in New York and enrolled in the Juilliard School of Music as a student of Sasha Gorodnitzki, later becoming his teaching assistant from 1979–1984.