It does sound harsh but if I were you, I would give her away. It is clear that you both will be better off without each other. Don't feel guilty. THere will be someone else to care for her.
I am, although, very concerned that they would put her to sleep but I sincerely hope that it does not come to that.
I understand the responsibility. That is why I have not taken the risk of adopting a dog although I have been wanting to have a pet for a while. I think it is not fair to the animal to live with me while I am not in a healthy place.