You just had your cat or dog vaccinated. Any side effects?

My best friend’s cat got sick a few days after being vaccinated. The cat will purr when you pet her but is eating very little and doesn’t want to run around anymore. She is staying on a bookcase shelf. My friend is upset and she herself came down with an illness a week or less after she, too was vaccinated for flu. It went away but came back. She vows to never have another flu shot. My last flu shot was in ‘89, I got very sick and have not had the shot or the flu since.