Transmission jerks from 1st to 2nd gear after car

That trans is a 4l60e. It has what is called a pressure control solenoid that as the name indicates controls the pressure in the trans. When the solenoid fails, it defaults to high pressure so the unit will not ship. It will cause harsh shifts. Most electronic items that are near failure will begin to show shut down failure when they get how and work when they are cold. This may or may not set a code. Look for a Pressure Regulator code

To replace it you have to pull the pan, and I am not sure, but you may have to pull the valve body. I do not recommend an armature do this. It is best to find a independent shop that specializes in transmissions and has a good reputation and have them do the work.