Blackheads, or open comedones, occur when pores on the skin get clogged open by dead skin, bacteria, oils, and other debris. The severity of blackheads is determined by a lot of factors, but definitely some people's skin is genetically more predisposed to them. Unfortunately, there is no definitive cure for blackheads, like a surgery or something to remove them permanently. This does not mean, however, that there is nothing you can do.
I would recommend that you see your primary care doctor
or your dermatologist
about this issue. They will be able to help you come up with a plan for keeping the blackheads under control.
As you already known, the basis of blackhead control requires keeping the pores clean. This includes daily washing of the face with a mild facial soap, gentle exfoliation, and avoiding any thing which might clog up the pores (like makeup).
In addition to these simple measures, in persistent cases like yours it is very helpful to add
comedonolytics, which are medications which strip away the dead skin layer, leaving the pores clean. Your doctor can determine which of these medications would be best for you to start with and prescribe it for you.