Maximum watts you can pull from an Arduino Nano

Almost any relay will require more current than can be drawn safely from the microcontroller. I hope you haven't damaged your MCU. Best practice is to limit pin current to 20mA, but there are also aggregate maximums per port so every pin cannot necessarily deliver 20mA simultaneously. See the datasheet for details.

I'm not familiar with your particular relays, and I didn't look them up, so I don't know what voltage and how much current they require, but the good news is that many relays can be driven using a simple bipolar junction transistor.

Simple one-relay circuit here. Note the flyback diode. This is included in the ULN2003 as already noted.