07 Impala rear driver side brake light and turn signal does not work, but when I checked the bulb it was working just not when I press the brake. The left turn signal on the dash also blinks rapidly.

There is a module on the passenger side behind the rear wheel mounted to the body. It goes bad. On the drivers side is where the grounds are located, on or close to the frame. Check these first.

take it to a body shop

Fast flashing dash signals mean there is a bulb issue-DEFINATELY!

The brake light side of the bulbs is powered by the brake switch and travels thru the turn signal switch.
If the third brake light works, I would guess the problem is in the turn signal switch.

Any idea's ? Yes , learn how these system's work ! Looking at wiring diagram's to see what all is involved in the electrical circuit's for the brake & turn signal lamps . Plus learning how to test electrical circuit's with a DVOM - digital volt ohm meter .
Electric Testing Techniques You Need to Know
Testing is how to find this problem , not going by someone guessing who has not even looked at the vehicle ! Free wiring diagram's here http://www.bbbind.com/free_tsb.html Enter vehicle info. year , make , model an engine size . Under system click on lighting ,then under subsystem click on stop lamp or turn signals . Take your DVOM an at the rear right stop lamp bulb test for B+ voltage , check ground side . See which side of the circuit has the problem . Mastering Voltage Drop Testing with Pete Meier and Jerry Truglia

Does any lights on the right side work? It sounds like the ground connection to the assembly is loose.

Sounds like you need to replace the drivers brake/tail light.

you replaced the bulb with the wrong one i.e. a two filament bulb with a one filament bulb

Two issues here, you will need to replace the flasher. this will correct the erratic turn signals.

Concerning the brake light. Make sure the bulbs are in working condition and, check the wiring harness for faults as well. if the bulbs and wires arr OK, replace the brake light switch.

You can test for proper current by pulling the brake light bulbs out the socket and, use the copper prongs inside the brake light socket for testing. use a volt meter and, hit the brake pedal and, see if the meter registers a current. if not, replace the wiring harness.

Rear lights are double filament bulbs one side for the lights other side for the brake/turn signals so it still may be a bulb. Do u have a test light or volt meter you can check to make sure u have power there when brakes or turn signals are activated. Or just try another bulb.