My toilet backed up with no water
Those symptoms indicate that the blockage is likely beyond the trap that's built into the toilet bowl. It may be where the toilet meets the floor near the wax seal, or it may be even further down the line. If a plunger isn't dislodging the blockage (remember the goal is to suck up, not push down with the plunger), then you can get an auger that's specially designed for toilets (and I would recommend the longer version just in case your clog is further down the line):