The vomiting and diarrhea in cats is due to eating something disagreeable, eaten too much or too fast, are overly excited or nervous, have hairballs etc. If your cat is not sick then you can treat her at home.
Take away all food and water for 24hours and if she is feeling good then you can give her the little bland food.

 You need to call a vet, and decide if you need to take him / her in. The cat may have some kind of worm(s).