A ‘Sick Puppy’ is an endearing term to describe a person who struggles with their mental health. A strange but loving way of owning the struggles they have been through and being proud of where and who they are today.
First used in this context by singer/songwriter ‘Kings Elliot’ who herself struggles with borderline personality disorder, anxiety and panic attacks.
I've struggled with anxiety all my life, I guess that means I'm a sick puppy!