Burn-z

So I just bought a 2000 A6 w/. 2.7 it had a coolent leak that I fixed but apparently I didn't get the system bled out and still can't, every time it idles it overheats and now it started missing and in the process the aux air motor is now making a horrible noise when I start it after sitting all night but that's not what I'm worried about its the engine missing now that I'm very worried about it got very hot and you could smell plastic burning any ideas on where to start trying to fix???