Truthfully - if she is that miserable at your house - it's unfair to put her in any shelter (kill or no-kill). Give her more time - several months. If she doesn't adjust, IMO, it is kinder to euthanize her yourself than put her in a shelter (as realistically - no one is going to adopt her).
That being said I agree with others that she needs more time. I guess too I think that it's important to check what you are thinking & feeling while interacting with her. Animals can read so much through body language and tone of voice. Things that humans might never notice. Perhaps you are giving off a nervous vibe or if you are feeling sorry for her she is feeling sorry for herself. I know it's hard but spend time focusing on your emotions & get in the right place before going in the room with her. As others have said just sitting still or relaxing in the room with her may help.
Sending lots of vibes for improvement.