You grew up in America. You spent the beginning of your life in America.

It means literally what it says - that a person who speaks grew up in America. Raised is a passive form of the verb "to raise", which means "to care for something in order for it to grow and strengthen".

To be "raised" somewhere, means to grow up there. Maybe I was born in Britain, but I moved to Spain after a year. I lived in Spain and grew up there. Living there until many years later. I could say, "I was raised in Spain". The same applies if I spent most of my childhood growing up in America. "I was raised in America". Hope this helps