We do have a Patrick Carroll. His parents are Matthew Carroll and Anna Burns. My ggranndfather was born in 1856 in Indiana he had a brother Patrick and two sisters Hannah Mary Anna that are older than he but I don't have the dates. He also had a younger brother named Nicholas . Patrick didn't come to the USA until after the Civil War and settled somewhere in New York so this could be our Patrick. The date would make his father about 23 years old which would be about right.
It was common practice to drop the O' in the Carroll name.
I have from family lore that Matthew Anna either from County Wexford or County Wicklow , Ireland but haven't proved that yet.