A. No, you can't get the flu from the flu shot.
Since it takes about two weeks for the flu shot to work, depending on when you get your flu shot, it is possible to be exposed to someone with the flu and to develop flu symptoms because you got the flu about the same time that you got your flu shot. That it is why it is usually a good idea to get your flu shot before the start of flu season if you can.
But you can't actually get the flu from the flu shot because the flu shot is made from inactivated or killed flu virus that can't cause the flu.
Although you won't get real flu symptoms when you get a flu shot, some people do have a reaction to the flu shot, including soreness, fever, and aches. These symptoms typically last for 1 to 2 days and can mimic the symptoms of the flu, although the fever is not as high as you would get if you really had the flu.
Having one of these minor reactions to a flu shot is usually not a good reason to not get a flu shot in the future, as they are much more mild than real flu symptoms, which according to the CDC can include high fever, headache, tiredness, dry cough, sore throat, runny nose, muscle aches, and stomach symptoms.
1CDC. Key Facts about Influenza and the Influenza Vaccine.
2CDC. Key Facts about Influenza (Flu) Vaccine.