This particular idiom being in evidence since about the 1500s according to the Cambridge dictionary of American idioms.
The saying "as sick as a dog" has its origins in the fact that dogs will willingly eat almost anything and be very ill afterwards. (indeed often eating the very evidence of their being ill soon after they produce it.)
The idiom generally means "I feel as if I'm going to vomit," although it can apply to a general bad feeling while ill. The emphasis is on how you FEEL, not necessarily on how severe the illness is.
"After my mother at the rotten apples, she was as sick as a dog"
I am getting sick of answering your questions!
I feel sick because of you.
She was identifying me to check to see was I sick
the sick child was pitied
the nurse identified he was sick
Sick Em!
I was sick yesterday, but I have recovered.
The sick boy's face is very ashen.
The fact is, that you were sick of civility, of deference, of officious attention.
The component man was sick.
Didn't she have an orange shirt on ealier? He didn't want to go to school because he was sick. I didn't break the vase! i hope these are good!
parents often hover over there sick child