2003 Pontiac Grand Dam Gt

My wife has a 2003 Pontiac Gran Dam GT 3.4L V6. A few days ago my wife was out and tried to start the car and the service engine light came on and began to blink. (Prior to this the car was running well with no service engine light) The car was running very rough at this point so we shut the car off and I pulled the codes at witch four codes came up witch were: P0205, p0206, p0300, p0443. So I had the car towed to the shop and they said that they thought that it was the oxygen sensor but after that had been replaced they had concluded that the oxygen sensor was not the problem so they had placed the old one back in. Then they said that they restarted the car and it was running fine but then pulled it out of the shop and began to run rough again. At this point they were thinking that there was a short so they checked the wiring from the ecm (?) back to the oxygen sensor and could not find any problems. And needless to say they started the car and it began to run fine again so they told me to come and pick it up and drive it for the weekend just to see if it was a lose connection that was possibly there. So needless to say once I picked it up the service engine light was still on but the engine sounded good so I figured I would drive the car home and maybe the light would shut off. Well upon taking off and getting a few miles down the road the engine started to idol at 2000 rmp when in park or neutral. So I stopped and pulled the code and got P0443 again so while I had the scan tool connected I cleared the codes to see if the light would come back on with the same code or with multiple again. The service engine light stayed off.
So the high idol continued for a few miles I also did try to restart the car and the problem did persist. About 5 more miles down the road the car started to overheat and the resivor had overheated. So at this point the engine sounds good it is not running rough but is really high idol. The check engine light did not come on since I cleared the codes in that short drive but I do not want to drive it because of the overheating. I do know that the coolant level was good when we started the car.

205 and 206 indicate a misfire on 5th and 6th cylinder. 300 indicates multiple/random misfires detected(related to the 205 and 206 codes). P0443 Evaporative Emission Control System Purge Control Valve Circuit.
My prognosis is that the misfires are causing you to run lean/rich, which is causing the p0443 code. Minimum you’ll need to replace the spark plugs and wires. But, for the love of bob, don’t take it back to that shop. Any COMPETENT mechanic wouldn’t just throw a part at it and call it fixed.