Oil coolers are separate from radiators. Usually in front of the radiator. How much oil are you seeing in the radiator? You had the GC for a long time or just got it? ...
Knowing very little to nothing about your case, I would have to guess you may have a blown head gasket. Many repair shops carry a pressure testing rig for the radiator (or you can get one of your own if you do much work yourself via Amazon around $50. Very easy to use.) Use the pressure test rig to see if the radiator and cooling system are holding steady pressure OR may be leaking down. If leaking, you likely have a blown head gasket. There are other test gear that let you see if combustion is getting into the cooling system etc. Anyway, I would start with the pressure test.