I see in www.findmypast.ie
that Edward Fallon was a Local
Authority Official in the Ballymoe area in the 1880's and 1890's.
Ballyglass is mentioned, but there area many townlands of
that name in County Galway. Ballymoe Barony appears to have
"Middle, West etc"
In relation to the teaching profession: The National Archives in Dublin have records going back to the 1860's. It requires some research to see if the particular school is actually on record. It takes approx. three days notice to have the records made avalable.