When you get the SHOT you are getting a vaccine that contains either inactivated influenza viral particles OR one that is recombinant. What does that mean?
An inactivated vaccine is one where the viral particles are killed and therefore unable to infect (get you sick).
A recombinant vaccine is a little more complex but still unable to cause disease. This vaccine uses an attenuated virus (altered so it is no longer able to cause infection), which introduces it’s genetic material to cells of the body. These vaccines only mimic a natural infection and do a great job of stimulating an immune response. (That’s the short version; these vaccines are a little more complex than this.)
Anyway, these two types of vaccines are safe and unable to cause infection. However, they can cause some side effects due to the immune response caused in creating antibodies. These common side effects include soreness at injection site, low-grade fever, headache and muscle aches. Sometimes these will be accompanied with cold-like symptoms.
There is another vaccine for the flu and that’s the nasal spray (flumist), which contains the live (yet weakened and unable to cause disease) virus. Currently in the US the CDC is not recommending the use of the nasal mist during the 2017-2018 season because of concerns about its effectiveness.
In short, you can not catch the flu from the flu vaccine, only some mild symptoms as the body is making antibodies to the viral particles or genetic material.