Flu shot

So my baby just had her 9 month check up yesterday. The only vaccine she was given was the flu shot. I was not thrilled about giving her this shot, bc I’ve not gotten one in 7 years and not once got the flu. I’m not a fan of it, but I understand that her immune system is not as strong and needs some help, so I decided to give it to her. Today, she is so sick! Running a low grade fever, throwing up and just overall feeling crummy. The pediatrician’s office is telling me it’s not from the flu shot, however I’m finding it very ironic that she’s sick the very next day, and she’s never been sick yet! Has anyone else’s babies had this?