Can anyone tell me why code 11 appeared on my dash when I shut car off?

 

No idea. OBD II codes are 3 to 4 numbers.PO 0011 would be a VVT code.but it would not be on your dash. It is read with a code scanner, which you might have done, to see if anything is wrong.

BTW, have you replaced your ignition switch? Cobalt's have a tendency to shut off if it is touched while driving. The dealership HAS TO DO IT FOR FREE too. Its a safety issue and people died due to this issue leading to lawsuits. Everything goes dead including your power steering and it can cause a crash. Chevrolet will gladly put a new improved ignition switch in your Cobalt. If the dealership says otherwise, contact the NTHSA.