When I get a zit, I don't wait till it has a white puss head. I just take a Dettoled needle and prick it and then I squeeze it with my fingers , this damages nearby skin and then leaves a dark mark around with a white skinless crater.
I MUST NOT squeeze my zits, keep on applying BP until the zit gets a whitehead, even if it takes more than a week !
If I do get a dark crater, use BP on it at night to dry up the skin and to also speed up skin regeneration underneath. Then, use a microdermabrasion cloth and gently wipe the craters to remove much of the dry dark top-layer skin.
Finally, use manuka honey to repair skin colour to what it was before.