You probably either have a faulty sensor or gage cluster. The best way to test this is to remove the oil pressure sensor at the back of the block behind the intake and install a mechanical gage to make sure oil pressure is ok. If oil pressure is okay, then you will need to have a sweep test performed on the gage cluster to make sure the gage is functioning properly.This has to be done with a scan tool. If oil pressure okay and gage okay, replace the oil pressure sensor.
Has there been a recall on the gage system problem? This issue sound like it has to be done in a GMC shop? What's the cost range for this type of repair?