I have a one year old zu (meka) who is usually a happy and playful dog. Yesterday I brought home a new puppy meka has become very upset and depressed about this I knew this would happen but not to this degree she has made herself sick she is vomiting shaking and won't come near the new pup.
She is not eating or drinking, I am very worried about her
Any help would be great

Lavish attention on her. Keep the puppy away from her. At a year old, she is young enough she should adjust and accept the puppy eventually playing with it. If the upset stomach goes away in a day or 2, it won't hurt anything.

The housebreaking sticky may help with the new puppy and includes tips on cleaning up vomit, https://www.askmehelpdesk.com/dogs/information-articles-our-dogs-expert-labman-53153.html#post251809