The best secondary sources I can recommend for specifically Ireland are

Foley, Caitriona. The Last Irish Plague: The Great Flu Epidemic in Ireland 1918-19. Irish Academic Press, 2011.

Milne, Ida. Stacking the coffins: Influenza, war and revolution in Ireland, 1918–19. Manchester University Press, 2018.

Generally for references I'd start from those and "follow the trail" of primary sources they mention. A quote from the Milne book to illustrate:

By 10 June, a journalist at the Belfast Newsletter reported an unusual outbreak of illness in Belfast, mostly among soldiers and female factory workers. The somewhat self-contradictory headline 'An epidemic in Belfast - no cause for alarm' expressed much of the tension as people kept a watchful eye on illnesses developing during the war.

If you want to get ambitious, there are a fair number of newspapers that were in print at the time as listed at the Irish Newspaper Archives; note that the Irish Times is not included but they have historical archives at their own website. The other national papers that were running in 1918 are

Belfast Newsletter

Freeman's Journal

Irish Examiner

Irish Independent

Sunday Independent

although there are quite a few local ones as well.

(Also, the newspaper archive site is for-pay, so I'd probably check with a library if you can.)