Without being too personal, it's difficult to answer.
The workhouse was one place girls could go to have birth if they were not married, Church parish records would not hold that information. When I worked in the R of I (a long time ago) national insurance numbers were only issued to children born in wedlock, youngsters used to come to the UK to get our NI numbers, return and transfer them to their own country. You obviously have access to Websites, try Castlebar, the county town of Mayo, and see what you can find
