P0446 is “Evaporative Emission Control System Vent Control Circuit Malfunction”.
Normally I’d agree with Cig that it would not cause lurching, but if the “malfunction” was of a nature that it prevented the gas tank from breathing in to replace the gas that’s being pumped out it could allow a vacuum to develop in the airspace in the tank sufficient to prevent the pump from being able to provide sufficient gas to keep the engine running smoth. That would cause lurching and chugging, and could feel ike a tranny problem.
Generally it’s a good idea to start by fixing whatever is causing the light, then see if the other symptoms are still apparent.
I’d tend to avoid any mechanic that told me to ignore a CEL because it was “only” the oxygen sensor. No good can come from that. Only bad. At this point i’d recommend finding a reputable local shop, telling him the whole story, and having him diagnose and fix eth cause of the CEL. If your other problems don’t then disappear, you’ll have lost nothing. But I’ll bet they will.