Sometimes my car doesn't want to shift from 2nd to 3rd gear.

Nope. That' "limp mode" to allow you to drive it slowly to a repair shop without needing a tow truck. You have to turn the ignition switch off and restart the engine to get it out of limp mode.

The Check Engine light should be on too indicating a diagnostic fault code was set in the Engine Computer's memory. That will be code 700 meaning there is a different code in the Transmission Computer. That code will be the starting point.