Yes, P0038 is related to the heater present in the upstream o2 sensor (also called an A/F sensor - it is a sensor before the catalytic converter so closest to the engine). The heater is not functioning. It needs that heater to increase its sensitivity. That is a problem. I believe on your car it is run through a fuse so check your fuses. If not, it could be the connection to the A/F sensor or involves replacement of it.
It is not related to not being able to move your stick to park, tho. If that transmission shop is suggesting it is related, they are full of something.
There's an interlock that you can access with a small screw driver through a hole next to your stick. It is usually described in the user manual, I believe. The problem may be related to that interlock or possibly your brake switch. The brake switch needs to be activated by pressing the pedal for it to come in and out of park - if it is defective, it won't let you do that.
That screw driver trick should let you move the stick to park. You may need to bring that screw driver with you until that issue is fixed because it will likely not let you move out of park.