You do have to make certain that the sensor you bought is one that's actually compatible with the MB TPMS system. I recently installed four new aftermarket sensors in my new wheels, and all I had to do was install them on my GLK and drive a few miles. They automatically sync'd with the vehicle, and were accurately reporting all four corners. I just mounted my snow tire wheels yesterday, and within 3-4 miles, the "new" (old) sensors were all reporting properly as well.
I can only wonder if you got one that wasn't capable of auto-sync'ing with the MB TPMS system.
FWIW,
for the new wheels. I know they're unavailable, but FWIW were around $80 delivered for four, and seem to last many years (based on reviews).