First of all welcome to the community, It's great to see that you are interested in finding out more about your Great Great Grandfather Daniel O'Connell.
The most helpful thing to know when searching for old Irish documents is how the records are stored. Before 1864 the only records kept were in the form of church and parish records (so usually baptismal records instead of birth certificates, and burial records instead of death certificates). Many of these have regrettably been lost over the years, however, all the surviving records have been sorted into county based genealogical centres
. In 1864 civil registration was introduced in Ireland, which is when we started seeing the formal registration of births, marriages, adoptions and deaths. These records have been kept at the General Register Office of Ireland
(GRO), to this day. Additionally, once Northern Ireland was created in 1921, we saw the creation of GRONI, the General Register Office of Northern Ireland
. This is important, because anyone who lived in one of the 6 counties that would later become part of Northern Ireland between 1864 and 1921 would have had their records stored with GRO, but if they were born or lived in Northern Ireland after 1921, then their records would be with GRONI.
I have tried searching for the location of Polgorm or Polgourm and unfortunately haven't been able to find the town. This is where documentation plays a very important part of tracing your ancestors.
Maybe some of our fellow community members may have some more suggestions on the actual location.
Best of luck in your research,