FRom this description it maybe that you are trying to maintain your balance by your arms, attached to the your hands, which are holding the handle bars.

If you are, this could explain your experience. Balance is maintained by your forward motion and slight shifts to your boy weight against the seat, not by the position of your arms.

The best way to experiment and develop your confidence, may be by locating a gentle downgrade, and just coast straight, without pedaling, keeping relax grip on handle bars with your hands. Y0ou will not be pedaling which can shift your weight and give sensation of loosing your balance.

This may require several attempts, but each time, try adding some pedal strokes, and if you feel you are loosing balance, stop pedaling and regain composure. Also lowering your seat may help as well, to height your feet can easily be placed on the ground. If adjusted for proper leg extension, you may feel it is to high and fear of loosing balance is cause of arms for balance control.

I commend you for learning and wish you all the best.