Well before getting into elaborate possibilities, I'd check two things.
One, that your electrical connection to your oil pressure sender might have come loose and is grounded, or b) that the oil pressure sender (sensor) might be defective. You may have to verify by using a regular oil pressure gauge screwed into the aperture where the oil sensor normally resides.
Two, that your new oil filter is completely plugged up for some reason.
Other possibilities might include the oil pressure relief valve if your engine uses this device. These relief valves are pretty reliable, but you never know the weird things that happen with cars.