It is still possible your family came from Cork. I believe it is the largest county so it makes sense that a good many people came to the US from Cork. Although a death record, cemetery stone, or obituary might have the county of origin, often the best source to check for county is a naturalization record. If your family came to MA, you would probably find the naturalization record at the regional National Archives in Waltham. In my own family, the number of children varied. Usually, if there was only one marriage, the limit was about 12 children (again, in my own family). I found that with my poorer families and with families who lived during the famine, there were often about six children. Perhaps immigrants had better food and thus better nutrition when they arrived in the US and that led to bigger families??? Good luck.