If the bearing service you mentioned was done by removing the hub from the spindle and packing the bearings individualy, most likely the mechanic just failed to install the grease cap back to it's seated position and it came loose and just needs to be tapped back into it's seated position.
Just pumping grease into the bearings through the nipple should not have caused it because the excess grease just comes out around the outer edge of the hub and into the grease cap, then usually the excess is wiped off and the rubber insert is put back in place. No pressure could build up at the cap.
For safety's sake I would jack up the axle under the spring hanger and roll the tire checking for excess play as described previously just to make sure the outer bearing is ok for now. If no excess play then it will be fine to tow it home.