Definitely sounds like he has eaten something toxic. A lot of plants will cause these reactions if ingested. Call your vet asap, and good luck!
She could possibly have eaten something outside in a toxic form. (Plants, etc) This would cause the panting and shaking. If she has somehow gotten into caffeine, or nicotine(eating chocolate or chewing up a cigarette) she would act like this also. Call your vet, explain the symptoms, and take his advice!
Yellow bile could mean that the dog has an empty stomach and needs to eat something. If he won't eat anything he probably should see a vet. Most of the time, though, it's having nothing in the stomach that causes the yellow bile vomiting.