Am "I" my attachments?

[Holygrail]

If I am attached to a pretty rock, do I consider myself that rock and not the other things that I'm not attached to? 

[OneHandClap]

"You" are always the same thing "you" have always been—a looping, self-referential pattern of grasping that manifests and self-sustains through clinging. In Absolute reality, there is no self to be spoken of. But in relative reality, yes, your self-image can be literally anything, including (or containing) attachments to inorganic objects. 

[Inliytened1]

1 hour ago, Holygrail said:

If I am attached to a pretty rock, do I consider myself that rock and not the other things that I'm not attached to? 

As a finite being you have bias towards some things and not others.  If you had zero bias you would be infinite (total Oneness) and selfless.  In other words, you as a self would be dead.