Both are correct :) She has my heart. She is my heart. It depends on the context of your feelings. And yes of course, there are many other words to describe your feelings more effectively :)

You can say, "she is my heart and soul"

The first one "She has my heart" you COULD say "She is my heart" but to me it sounds kind of wierd. You could say, however "She is my love" :P Sounds more normal haha.