Can You Explain This About Oily Skin?

Every time I squeeze my nose, even if there are no properly visible blackeads, oil comes out in a sort of toothpaste tube style (ewww lol). And I realised that it happens when I squeeze the corners of my mouth, and my chin! It's horrible. I wash my face with a blackhead clearing scrub, and sometimes a clinique facewash, but the facewash makes my skin really dry even though the oiliness goes away for a while. Does the oil squeezing thing happen to you? And how can I stop it, or is it a teenage skin thing? thank you for reading :)x