Hello, my name is***** and I have over 20 years of experience as a veterinarian. I am very sorry to hear about your girl Daphne shivering, and not wanting to eat.
Is she lethargic?
Is she running a fever (rectal temperature greater than 103F)?
How long has she been with you?
Did you change her food from what she was eating at the shelter?
Dogs will often shake when they have a fever, are anxious or are feeling nauseous.
In her case with her lack of appetite and no fever I suspect that she is nauseous.
Possible causes of nausea include a systemic infection, change in diet, dietary sensitivities or allergies, or eating things that they should not like too many fatty table scraps or garbage, bones etc., metabolic organ failure (kidney or liver disease), pancreatitis, inflammatory bowel disease or even infiltrative cancers are possible causes as well.
Has she eaten anything she should not have recently (toy pieces, bones, garbage)?
Any changes in food or treats?
You can give her acid reducers to try and settle her stomach. Either:
1) Pepcid-ac (famotidine) at a dose of one quarter of a 10mg tablet per 5 to 10 pounds of body weight every 12 hours.
OR2) Prilosec (omeprazole) at a dose of one quarter of a 20mg tablet per 10 to 20 pounds of body weight every 24 hours.
These will reduce stomach acid and should help settle her stomach. These can be used for several days if necessary as they are very safe.
I'd also pick up her food and water for now.
A couple hours after one of the acid reducers are given you can offer small amounts of water or ice cubes to lick.
No food for 12 hours. Small amounts of water only.
After her food fast then start a bland diet of 1/3 boiled, lean hamburger (or boiled, white, skinless chicken) and 2/3 boiled, plain white rice. Give small meals several times a day. Feed the bland diet for several days, then start mixing in her regular diet and slowly convert her back.
If her nausea and lethargy continues then she may need injectable medication from her veterinarian to get her stomach upset under control.
So watch her for vomiting even with the acid reducers, blood in her stool or vomit, or a fever (more than 103.5F rectally), a tense painful belly or lack of appetite after her food fast and even with the acid reducer. If any of those occur it is time to seek hands on veterinary care.
Because she's a shelter pup she may have bee exposed to infectious diseases, so if you have another dog you may want to quarantine her away from your other dog(s) until you know why she is not feeling well.
Please let me know if you have any further questions.