Hello, blackheads may take a long time to cease. We all have bacteria, sebum and dead skin cells which collect on our skin but for some people, this combination has a habit of collecting in the pores and oxidising, therefore turning black. I do occasionally extract blackheads if they're really bad, but only after an enzyme mask and sometimes steam. Not all salons will do extractions.
For home care, the trick is to treat this gently. I did used to use Biore strips on my own blackheads, which is the complete opposite of gentle. They're really harsh and they hurt, but I did get the satisfaction of seeing the blackhead plugs getting pulled out. I since learned that the key is trying to keep the skin clean with gentle cleansers, not to let the skin get dry. I also love using flower water such as rose water as they're v gentle to use as toners. Use face masks regularly, be careful with scrubs as the scrub particles can get into the open pores and cause spots. If you can get to have regular facials, this can help. I know with all my regular facial clients, their skins improve no end. You could maybe do a swap with a facialist?