Sissy,
You might try County Roscommon which is next to County Galway. My maiden name is Galvin and I found my family in County Roscommon. The Galvins are mainly in Cork and Roscommom. The Roscommon History and Genealogy Society has a website and they will do searches - for money, of course.
Last summer I went to Ireland and actually found the cottage where my gr. gr. grandfather was born in 1854.
When did your family immigrate? I do have a listing of all the Galvins in Roscommon in the Griffiths Valuation and can look for you.
Donna