Has anyone else experienced this skin problem or am I totally unique?

[Crusoe]

Please someone help me.
I keep getting what feels like little bumps under the skin. They don't itch but somehow I am very aware of them. They NEVER come to a head but eventually sort of break open. They are then absolutely impossible to heal until I have extracted a stretchy sort of white core or plug. You can't squeeze it out but have to pull it with tweezers. The problem is if you don't get it on the first attempt it sinks deeper and you have to wait a day or two until it rises to the top again. Once this core is out they heal really fast and the bump goes. They always go into a crater appearance prior to getting the core. Currently I have one that is wide and very deep I can see the core but can't get it. This one I have had for over 3 months and I have tried everything. Leaving it is not an option as it really will never heal and will split open on its own anyway.
My GP looked at me like I was an idiot when I mentioned it but I really am sick of these sores.
Please does anyone have any ideas

[MissBeaHaving]

Where are these bumps Op?
Body or face?
Can you post a pic ?

[MissBeaHaving]

If on the body have you heard of keratosis pilaris?

[Crusoe]

Sorry should have said they only appear on my face, usually cheeks but occasionally chin or jaw.

[Crusoe]

Unflattering pic here

[Knitmyshickers10]

Morgellons?