No. The flu shot is made from an inactivated influenza virus and cannot give you the flu.
"But my mom got sick..."
Some people experience body aches and fatigue for a short time after getting the flu shot, which is the body’s immune system responding to the vaccine.
It is also possible that you may be exposed to a flu virus shortly before getting vaccinated or during the 2 weeks it takes the body to develop an immune response after getting vaccinated. This exposure may result in you becoming ill with flu before the vaccine begins to protect you.