This sounds like you are dealing with blackheads, or something on that spectrum of skin problem. Blackheads and their like form when the pores of the skin become distended and clogged with dead skin, skin oils, and other debris. The result is unsightly pores clogged with dirty appearing material.
The first step is to stop focusing on squeezing the pores as a solution to cleaning them out. This is because squeezing causes damage and inflammation in the skin and may lead to infection or other problems.
To treat the problem, you should begin with washing your face daily with a good facial soap. You can add
to this an exfoliating preparation, such as one of many "microbead" preparations, or simply use a thick textured scrubbing implement like a loofah. Most of the time these two techniques will result in significant improvement.
If not, then your next line of therapy is a comedonolytic. These are chemicals that are designed to strip away the dead skin and other debris that clogs the pores. The two most common comedonolytics are salicylic acid and benzoyl peroxide; they are found in many of the over the counter acne
relief products that you can buy at your local pharmacy or beauty store.