What the hell are these things?!?

I have these weird circles that look like zits covering my skin. For a while, I thought they were zits, but now I'm positive that it is something else. If you squeeze them, oil will come out. Also, the skin covering them peals off without me feeling anything. There's literally something under my skin, making it almost rubbery in texture. It's the oddest thing ever, because I can remove several layers of skin in those areas with no pain. Now, they are spreading. Does this sound familiar at all? If you think you know, please tell me!