I've got you under my skin

What does "I've got you under my skin" mean?

It means that you have become so much a part of me it is as if you are under my skin. In short, it is one of the almost limitless declarations of love.

DFG

Everybody sing:

I've got you under my skin
I've got you deep in the heart of me
So deep in my heart, that you're really a part of me
I've got you under my skin