I've never seen a Chevette with a V-6! Is that an add-on engine, or do they do things different up there? :confused: :confused: :confused:
The early 2.8's such as the one I rebuilt from my Brother's Chevy Cavalier had chronic oil pressure problems, and among other things, we found an oil passageway from front to rear drilled off-center which was starving one of the main bearing journals for lubrication. He had bought the car with a bad rod bearing, and we drilled the passageway straight with an extended-shank drill bit, and installed a high-volume pump. No problems for the next 100,000 miles!
It sounds like you've got a major pressure loss somewhere, either a sticky pressure relief valve in the pump, or some other catastrophe. Pull the engine and dismantle it before you have a major failure, and look for oddball things like oil passage problems. The early 2.8's were not good engines!
Jerry