Sheehy was born in Tuam, County Galway, Ireland in 1889, the son of a local policeman.
After the First World War, he returned to Burma and was appointed to the Development Commission in Rangoon and in 1924 was made deputy secretary to the Burmese Government.
In 1937, Sheehy was transferred to Delhi and was appointed to the Central Board of Revenue of the Finance Department of the Indian Government.
[3] Following India's independence from Britain in 1947, Sheehy joined the Allied Control Council in Germany.
They had 3 children including Sir Patrick Sheehy (1930-2019), a former chairman of British American Tobacco.