She does look a lot like a chihuahua mix. Even if she was kept in a cage and malnourished she wouldn't be that small--she would be really, really skinny too, which she's not. She doesn't really look like a gsd to me.
I would throw out the food they gave you and never go back there. And I would definitely file a complaint against them and get the media involved. I would also get a lawyer involved and get your money back because it sounds like you'll need it to get her health again.
Some dogs do great on kibble but I always found that when I brought a foster or new dog home with health issues it was best to make food for them and add supplements until they got better.
Rafi didn't look too good when I brought him home but a good diet, exercise and supplements sure turned his life around for the better!
Ruth & the 4 Legged Rescue Gang
Rafi the malaroo
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Gio & Varda, the krazy kittens
....In my heart: