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You need to run a OBDII scan first. Since the light came on, the car has done a diagnostic and found a fault in the system. The computer has stored the fault in the memory.
You need to run the OBDII scan to find out what the computer has found. Typically this scan is $90, however if you drive to the closest parts store and ask them to run an OBDII scan and give you a print out they will do it for free.
The print out will tell you what you need to repair/replace.
If the car is having trouble changing gears and hesitating, you are most likely experiencing a bad transmission solenoid or transmission sensor.
The car has a bumper to bumper for 5 years/60,000 miles
You are within that range and this is covered under warranty.