look for births from 1864 to the 1950's and you should find Nora.
Tuam is likely the Civil Registration District and covered an area of 12mi. and why as indicated from the other posting, emigrants gave the town as where they were from.
She maybe born too late to be in the parish register information on line at www.rootsireland.ie
counties only collected till 1900.
Tuam is the Civil Registration District for the townland of Ballina in the Parish of Killererin.
I think the spelling of Killererin has changed but the
Tuam records for RC go back to 1790-1900.