Why is the overheating light coming on so soon

Hope this helps, do this VERY Careful, when over heating Turn ON the heater to full, does it cool down? does the water in the Radiator Boiling?. = water pump, (don't always make noise).
Not boiling?- Check and R&R Heat sending Unit Gage on the Radiator or somewhere on the engine maybe close to the Thermostat..

If you changed the sensor and added coolant to replace the loss, you may still have air trapped in the system so if you are sure the thermostat is functional (these fail pretty often), remove any pressure caps from the overflow or radiator and let the engine idle (while watching the temperature) to see if the coolant level is falling; if it does, the system still has air trapped in it but should gradually pump it through.

Overheating can be "boiled" down to a few issues:
*blockage: Something is stopping or slowing the flow. Main suspect is the thermostat. It is designed to open and close at the proper temperature so as to keep the engine at the optimum temperature range. They have a tendency to lock closed and cause overheating. Sometimes it's random. The blockage may be something like sludge or rust in the radiator or gunk that someone put in that does not agree with it.

*coolant/water loss. A leak somewhere. Blown head gasket, cracked head/block, hose, etc.
*pressure loss. This happens when the water gets to boiling temperature but is kept under control by pressure (pressure resists heat) and then something such as the radiator cap releases the pressure and the temperature rises. The coolant will also leak out and then the overheating will be due coolant loss as well. This is especially true with the Cadillac Northstar. The head bolts allow the head to lift off the block, ever so slightly, and pressurize the coolant system with exhaust gases beyond radiator cap pressure limits. It's usually when you accelerate or put the engine under load such as going up hill.

^check for exhaust gases in the coolant. smell it or buy a kit to test.
^get a new thermostat, or, test the old one by boiling it in water on the stove; see if it opens. I always get the "failsafe" kind: fails in the open position.
^check for oil in the coolant or coolant in the oil: grey sludge.
^check for leaks on the ground.
^test the radiator cap. some part stores have a way to test them.
^check to see if it's made by Cadillac. look for the word Northstar. If so, hold on to your wallet. There's a whole new world of overheating adventures.

the onlie last thing is to replace the thermostat. check the heater core/radiator.

REPLACE THERMOSTAT AND RADIATOR PRESSURE CAP.IF CAR OVER HEATING WHILE IN MOTION.MORE LIKELY ITS THE THERMOSTAT,LOW COOLANT IN RADIATOR OR COOLANT SYSTEM,BAD WATER PUMP,WATER PUMP WEEP HOLE IS LEAKING, WATER PUMP NEEDS REPLACING.CHECK ENGINE OIL,IF OIL LOOKS LIKE MILK SHAKE YOU HAVE LEAKING HEAD GASKET.IF CAR IN PARK AND OVER HEATS WHILE IN A LONG TRAFFIC LINE OR.BANK DRIVE THROUGH COOLANT FAN NOT TURNING ON, BECAUSE THE ENGINE COOLANT TEMPERATURE SENSOR FAULTY.CODE SCAN CAR FOR FAULTY COOLANT FAN RELAY OR FAULTY PCM. CHECK COOLANT FAN FUSE, AND HOT WIRE THE COOLANT FAN TO MAKE SURE ITS WORKING.IF COOLANT FAN DONT WORK WHEN HOT WIRED. COOLANT FAN NEEDS REPLACING. REPLACE BOTH RADIATOR HOSES, REPLACE THERMOSTAT AND RADIATOR PRESSURE CAP.BUY NEW COOLANT ADD 50/50 WATER AND COOLANT.IF ENGINE OIL HAS ANTIFREEZE IN IT.REPLACE ENGINE OIL AND OIL FILTER TO KEEP FROM LOCKING UP THE ENGINE.GET CAR FIX.DONT KEEP DRIVING IF IT KEEP OVER HEATING,ENGINE DAMAGE WILL OCCUR.I HOPE INFORMATION I GAVE YOU WILL FIX PROBLEM.PROBLEM COULD BE LEAKING RADIATOR HOSES BUT CHANGE THERMOSTAT THATS FIRST THING I WOULD CHANGE BECAUSE IF IT CLOSED, ENGINE WILL OVER HEAT AND CRACK CYLINDER HEAD OR CRACK PISTON, COOLANT NEED TO CIRCULATE THROUGH THE ENGINE TO TAKE AWAY THE HEAT FROM ENGINE.

Remove the top hose, unbolt the thermostat housing, remove old themostat and install new unit with new gasket. Replace top hose and fill with coolant. Be sure to re-check the coolant level after start up, beore you drive it anywhere, to eliminate any air pockets in the coolant.

First look for signs of coolant leakage at the water pump, radiator hoses, thermostat, transmission coolant lines, and intake gasket. If you're leaking at the water pump replace it. If you have no coolant loss check to see if your coolant fan is coming on. If all is fine then you probably have a faulty thermostat. If it still overheats you may have a blocked radiator core.

looks like you have done everything but the problem with your car is that the cylider head gasket has gone have a look at the dipstick or remove the oil filler cap if it looks like mayo then 100% head gasket has failed you said no water on the floor so it must have gone into engine only way this can happen is head gasket failing, if you have put lot of water in to the cooling system then your sump will be full of oil water mix.

let us know your findings so we can help you more if you need it

head gasket