First of all: let's get the units right. Current is measured in mA. Battery capacity is measured in mAh (number of milliamps it can deliver continuously during some number of hours).
The use of your Arduino seems high. What is connected to the board?
The total current is larger than 1000 mA. So the power bank might get damaged, might have a current limiter, or might go into emergency shutdown, or it might deliver this current outside it's specs.
The computer USB will not deliver an infinite amount of current. It will also be limited but also damage could occur at very high currents. Maybe you should not use your computer USB port for experiments (as it is pretty difficult to replace it). You would better use a USB phone charger. But not all chargers may deliver currents higher than 1000 mA. So have a look at the specs.
So my start would be to find a charger or another power supply that can deliver 2000 mA and see how that goes.