I am sorry to hear you are worried about your kitten. My name is Rebecca. I am a veterinarian and will do my best to help.
How old is she? Are there other cats in the house?
She may be missing her mother, or other kittens. Some kittens are naturally bold, and will be eating and running all over your house in the first 5 minutes, and others are more shy, and take days or even longer to adjust to the new home. I once brought home a kitten that stayed behind the refrigerator for a week.
I usually start new kitten in a small room, like the guest bathroom, with the litter, food and water and a bed, and let them show me how much they want to come out and interact with the rest of the people or pets in the house. If there are other cats in the house, I block and tie the door so that only the kitten can fit through the door.
Keep offering to play with her with strings, little light balls, and catnip. If she seems sick at all, or continues to not eat, you might want to have her checked out by your veterinarian to be sure she is not ill.
She probably just needs some time to adjust, and you just have to be patient and not push her too much. If she is really young, and was taken straight away from nursing, she may have to learn to eat, but a healthy kitten will not starve to death.
Let me know how she is doing and what other questions you have. Rebecca