To start off with dint touch your face,i am suspicous you are picking and trying yo squeeze face,stop as it makes it worse.
the most obvious solution to turn to is benzol peroxide topicals but oral anti biotics from your dr is a good choice.
anti biotics kill acne causing bacteria,no bacteria = no acne.
you got a lot of blackheads that need to be extracted,try not to do it yourself,wait for a good solution that will naturaly get rid of them,i think salicylic acid is goid for pore cleansing and hopefully that could dissolve and rid your blackheads,you can get salicylic washs for your face.
theres steaming your face to open the clogged pores.
loads of good advice on these boards and am sure someone will come along and chime in.
Personaly what would i do?go to a dr and ask for oral anti biotic such as lymecycline and fo the course and see what happens,it should clear your skin up.
go buy a salicylic face wash (cant suggest one so do google) use that for a week or two and see if it clears them clogged pores and blackheads.try and break down the dirt and see if normal washing with the salicylic face wash clears them.