dotgirl has already covered this, but you really can't get sick from a flu vaccine. It can give you some side effects that are flu-like, but isn't the flu and isn't contagious. There are a ton of articles about this, but here's one I just quickly googled up, from the CDC, who I think are fairly knowledgable in this particular regard. :)
no subject
http://www.cdc.gov/flu/about/qa/misconceptions.htm