Clogged pores, even steaming doesn't help!

I have very stubborn clogged pores, they are all over my face but are most visible on my nose and T zone in general, including my chin.
I have tried every face cleanser and exfoliator out there (daily, by the way), I've tried steaming multiple times, nothing seems to work. They don't budge. If I squeeze (and it's very hard to get anything out), pus comes out just as it would if you were squeezing a blackhead...except not half as easy. I do try not to squeeze though.
This is probably why I'm prone to spots and pimples, all this sebum in my skin, but I'm at a total loss as to how to unclog - everything just doesn't seem to go deep enough. There's even little black dots that look like blackheads along my lip line that don't go away. I feel ugly, it's really getting me down. Please help.

[loiloi]

Hi. Cleansing and exfoliating does not, on its own, clear acne.
See your doctor for one of the many effective products available. A topical retinoid such as Differin will unclog pores and clear acne spots and blackheads. A course of oral antibiotics such as Oxytetracycline will kill acne-causing bacteria on the skin. Female acne patients will also benefit from taking a combined oral contraceptive pill such as Dianette or Yasmin, since the oestrogen they contain blocks the action of acne-causing hormones such as testosterone.
As you live in the UK, you can get these products on prescription for just £7.20 each.
Don't squeeze spots, this spreads bacteria under the skin leading to more spots. It can also result in delayed healing time, secondary infection and even scarring.
Eloise.