Thanks so much for reaching out here! It looks like you've already found out a great deal about your ancestry, and I'd love to see what I can do to point you in the right direction.
Before 1864 records were kept in the form of church and parish records; while some of these have regrettably been lost over the years, all the surviving records have been sorted into county-based genealogical centres.
Have you by any chance been in touch with the centres in Cork yet? They might be able to tell you more.
You can also search through the available online records, and I personally always like to use the Irish Genealogy page
. :) I hope some of our members who are experts in genealogy will be able to provide you with more helpful tips and information.