NEED Help With Servo motor
Your conclusion is correct. The servo motor is asking a lot of current.

You need a power supply that is more than 2amps. Connect the grounds (the servo black wire to the Arduino GND). Don't let the current for the servo motor go through the Arduino board. Use wires for the servo motor that can handle high currents. Don't let the power for the servo motor go via a breadboard, because the small metal contacts of a breadboard are not for high currents.

Can you get a smaller servo motor?

Could there be something wrong with the 2 A power supply? Is it a certified and good quality power supply?

Tower Pro does not tell what the stall current of the MG90S is: www.towerpro.com.tw/product/mg90s-3/