Oh my goodness, I have been wondering my whole life what these bumps under my skin are. I thought they were like little white-heads or something, but it's not until years later I realize they are oil deposits underneath my skin. It drives my crazy, because they would always come back after vigorously scratching at them -_-" (i know it's done horrible things to my skin). It bothers me insanely!!
I'm not sure if this is true, but I'm guessing it has something to do with how much oil your body produces. For me, I oil up pretty quickly. And when I say oil up I don't mean shine; I mean like enough oil to fry eggs on my face. haha, funny? not really ><" you can imagine how disgusting that feels. But, I've read online that you can prevent it by washing your face more frequently and using microdermabrasion kits to rid of excess oil underneath your skin. But to be honest, I've been washing/oil-blotting my face like 3-5 times a day whenever it oils, but things haven't changed for me.
You can try what I recommended, but tell me how it goes. Maybe ask your dermatologist. If you've received any tips that work, please let me know. I'm desperate to get these things off my face. :(