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First time posting on any forum like this so I hope this is the right place to post!
I've had two skin problems on my chin since I hit puberty, at least 10 years if not longer, and I've not been able to find anything that sounds exactly like either of them yet.
The first are these firm, flesh-coloured (maybe slightly pale) lumps about the size of a regular spot that develop on my chin, mainly along the edges. (The redder lump closest to my mouth is regular acne)
I do get cystic acne on my chin occasionally and these feel similar to the cysts after they stop being painful, but there's no pain or pus/blood, and they haven't gone away in years. They're not squeezable either.
The second chin problem is the area below my bottom lip and the bottom area of my chin always has blocked pores full of sebum. I pushed my tongue against the inside of my mouth to make them more visible. It looks like a mix of tiny plugs and more like blackheads closer to the edges of the area.
I do get blackheads/whiteheads/wide pores on my nose and cheeks so part of it is my skin type I'm sure, but no amount of cleansing and exfoliating ever gets rid of it on my chin.
When I smile and the skin gets pulled tight it's very obvious to the touch and you can see all the individual 3D lumps, which has been embarrassingly pointed out to me before when they first started developing.
Again, exfoliating doesn't seem to help, they feel very deep and the skin almost waxy. I can squeeze some out and clear the pores that way but they return the next day.
Both problems haven't changed much despite living completely different lifestyles and trying different cleansing methods all these years. Currently I use a baking powder scrub, a cleanser, an anti bacterial salicylic moisturiser and a vitamin E toner which have helped make my skin softer and less flakey but not helped with these problems at all. I also only wear make up a few times a year.
I can't afford to go to a dermatologist or expensive treatments so any advice on what it might be would really help!
I recognise those problems, I use to have both but to be honest I don't know what healed them as I've tried so many things over the years. You might want to try rosehip oil, it works really well for me. It hydrates my skin and also gets rid of my cystic acne. Don't worry about it being an oil, it doesn't make me break out and doesn't make my face oily. I use it at night, 3 times a week. It might also be a good idea to try a gentle scrub to get rid off dead skin.
It looks exactly like what I have - bad closed comedones. Especially the ones in the very center of your chin. CC's can also get surprisingly big. I can tell they're CC's by the pale covering of skin and slightly white color beneath...and if you squeeze them, does a white string of pus come out? That's definitely a sign. I HATE having so many CC's as well, they're extremely difficult to get rid of. 
I'm currently trying to find a solution...a lot of people say AHA/BHA gel or cleansing pads work but I have sensitive skin so I'm worried. Exfoliating can also help. But having a ton around the mouth/chin area points to acne driven by an inner imbalance. Can you start birth control?