Small female chihuahua; 8 years old. Dog is shivering,

Shivering can have several causes but is most often associated with pain, distress and/or fever. Coupled with vocalising when touching the ribs , I would worry she is in pain. Pain can also cause a reduced appetite.
It may be that she has fallen when you weren't around or has perhaps jumped from a height or twisted herself. We would hope if there was an injury that it is just a muscle strain but small dogs can be prone to e.g. slipped discs in the back so we need to be cautious. Is she able to walk as normal (she's putting weight on all legs and not arching her back)?
As she's not neutered we always have to keep an eye out for a uterus infection called pyometra. Symtpoms are variable but we would want to monitor for any discharge from the vulva, increased thirst or a swollen/ tender abdomen.
I agree, a viral infection is possible, though this wouldn't explain the rib tenderness. However, it may be that she is stressed and so is just being 'reactive' when touched.
As it has been a day since she's eaten and she's so small we would want to ensure she does not become dehydrated nor develop low blood sugar. Check hydration by ensuring her gums are pink and wet rather than sticky/dry.
Offer her some tasty food such as warm chicken and rice. If she is not drinking, offering the warm water the chicken is boiled in might be a winner. You could also syringe some water into her mouth if she shows no interest.
If you feel she is deteriorating or is in pain/distress, it may well be worth having her checked over by a vet this evening. They will check her from nose to tail, try to determine if she is in pain anywhere, assess her hydration and check for a fever. They may well give some pain relief if it is needed.