Where could this ancestor have arrived?

Its very hard for me to find where my great grandmother came from. I know she was an irish immigrant and arrived in America from somewhere about 1910-1920. I know she got to chicago fairly soon after she reached America and settled down with a Francis Gorey. Her name is Johanna Patrica Cantillon. The only problem is that she is really confusing. On some of the records I found of her she signs her name Johanna Gorey then others she signs Hanna Gorey some Hannah Gorey and some even has her name as Patricia Gorey. Also I'm not sure the spelling of her last name. I know Cantillon is how it is pronounced but I'm not sure if its spelled Cantillion, Cantilon, or some other variation. I don't know what port she came through, I've been just uming Ellis Island even though they don't have anyone in their records by that name. I'm lost and please don't tell me to go to ellisisland.org because that didn't help.