There are a lot of possibilities here.
Did you have an allergic reaction to that shot? Were you exposed to the flu before the shot had time to work (it takes about 2 weeks to develop immunity following a shot)? Did you catch a flu or flu-like illness that was not contained in the shot?
For people who are allergic to the flu shot, there are now flu shots available that are not made in eggs.
The flu vaccine can only protect against 3 (4, in some newer vaccines) kinds of flu. But there are many kinds of flu. Whether or not the shot will protect you depends on how similar the flu you are exposed to is to the (dead) flu contained in the shot.
At your age, the immune system is becoming weak. People over the age of 60 are especially prone to influenza and its complications. One common complication is secondary infections; your body's fight against the influenza virus leaves you susceptible to bacterial infection.
Thank you for your concern, but.... no thanks.