When I plug my vacuum in, the power in the living room turns off. Is it the vacuum or am I overloading the circuit?

You will need to do more investigation to know whether the vacuum itself is to blame or if the circuit is overloaded. 

Try unplugging some of the other appliances currently connected to the living room circuit. This will decrease the load on the circuit. If you can now use the vacuum without problems you can surmise that the circuit was merely overloaded. If the circuit still blows, try the next step.

Unplug everything else from...

You will need to do more investigation to know whether the vacuum itself is to blame or if the circuit is overloaded. 

Try unplugging some of the other appliances currently connected to the living room circuit. This will decrease the load on the circuit. If you can now use the vacuum without problems you can surmise that the circuit was merely overloaded. If the circuit still blows, try the next step.

Unplug everything else from the living room circuit and try the vacuum. If the circuit blows it is likely that the vacuum is damaged and causing the ground fault interrupter to flip. You may, however, want to try this in another room as well, to make certain the fault is actually in the vacuum and not the electrical outlet itself.