Now she is throwing up out of her butt, can I give her pepto bismo? If so, How much??

Your dog doesn't "throw up out of her butt." She has diarrhea. Is there blood in her stool? How much "raw chicken juice" did she drink? I have never heard of a dog getting sick from drinking a bit of chicken juice, so make sure there wasn't something else she might have gotten into. If it was just the juice runoff from one chicken and she is not showing signs of blood in stool, make sure she has plenty of water and allow her to continue to defecate until she has completely expelled what has caused her stomach to be upset. Since I don't know when this problem started, if the diarrhea lasts more than a day, call your vet and bring your dog in for an examination. Scoop up what you can of the diarrhea so that the vet can check it for parasitic infection and anything else that he/she deems necessary. As an FYI, never give your dog any medications of any kind unless the vet advises you to do so. So, call the vet. If he/she tells you it is okay to use pepto bismol, then use it.

I have to agree it sounds like more than just a little chicken juice. Yes, call the vet.

Whatever is wrong with your dog you should not give her pepto. Diarrhea/vomiting is how a body expels fluids that the body is rejecting. And giving something to keep it in is never a good idea.