A "get well" card is a common courtesy, as is answering people when they are speaking to you.
Detaching doesn't mean "being an ass."
You are swinging wildly from one extreme to the other. Treat her like you would a roommate, or the mail carrier. That's a good rule-of-thumb (would you not respond to the mail carrier if she was speaking to you?).
I think the card is okay, but nothing mushy or romantic -- just a simple acknowledgment.
