We have a strong and vibrant Irish community here in Indiana. I, my family and friends we're all proud of our heritage. There's lots to get involved in if you seek it out. If you don't experience it yourself does not mean it doesn't exist...
There's nothing wrong with being proud of your heritage. I know many people do identify with their heritage. But not everyone does, and it's okay not to as well. You were likely brought up in a family that sees the heritage as very important. I was raised in a family that did not. As a result of that, I've never identified as anything other than American.