There's no need to worry after your cat has been vaccinated.
If your cat stops eating after getting a vaccination, don't worry too much. Due to the side effects of vaccines, cats need to be in good health before vaccination. If a cat has a weak immune system, it is more likely to have problems after vaccination.
If your cat simply has a poor appetite, you can give it some digestive aids or supplements, either mixed into its food or given alone. These can help promote digestion, increase appetite, and improve symptoms like loss of appetite and anorexia. Observe your cat for two or three days after giving it the medication to see if there is any improvement. If your cat still refuses to eat and this continues for a week, you should take it to a veterinary clinic for examination and treatment. 
Precautions after a cat receives a vaccination
1. Cats should not be bathed immediately after vaccination. Because their resistance is relatively weak after vaccination, it is best to wait a week or half a month before bathing them to avoid them getting cold or frightened and becoming sick.
2. After vaccination, keep your cat warm and avoid taking it outside to prevent it from getting infected with bacteria or viruses.
3. Pay attention to feeding your cat after vaccination. Cats may experience a loss of appetite after vaccination. Do not force your cat to eat during this period. Give your cat time to adjust and recover. Do not feed your cat overly greasy food at this time.
