S.Z.
I would suggest doing some research online to learn all sides of the issue in making an informed decision. I often use www.babycenter.com which has many articles from pediatricians and other medical professionals.
From all that I've learned of the flu shot, it is safe. The shot is not an active living virus, (which I had originally heard it was). The nasal spray vaccines are the ones with a weakened live virus, but children under the age of 5 are not allowed to take this form. Complications from the flu virus in children are far more severe than in an adult, that is why I vaccinate my family - including us parents:)
Hope this helps!
S.