If your GFCI tester was well made and functioning properly, you were right - it would draw so little current it wouldn't create any dangerous situation, and it certainly wouldn't draw enough current to overload any wires or to trip any breakers.
GFCI protection is supposed to trip with 4-6ma of current imbalance. A good tester would test by creating a leak / imbalance of just 6ma - just enough to trip the GFCI protection. It also would be made so that it was safe if it was inadvertently plugged into a circuit with no GFCI protection present, or non-functioning GFCI protection - after all, it's a tester, that happens when you're testing.
If it's junk, or even if it was high quality but it's broken, it's possible it may have shorted hot to ground without any resistor to limit the current to 6ma. That would trip a breaker, hopefully the branch circuit breaker, but it could also trip a main breaker in a panel or a breaker feeding a subpanel.
If it was the main breaker for the whole house, and it was functioning properly, tripping the breaker would shut off everything, not half the house. A tripped breaker feeding a subpanel is likely with half your power off.
Locate all your panels, look for a tripped subpanel feeder, switch it off and back on.
If it keeps tripping, don't keep resetting it! Call an electrician and get the issue resolved. It's always possible there was some coincidence or something unusual happened.