Are blackheads ultimately a problem with the pores as well?

Ever since I was young, the sides of my nose have always been covered in black dots known as blackheads. Makeup covers them up a bit, but up close, they still look like sesame seeds. So, when I don't wear makeup, the center of my face looks terrible. When I was younger, I used to squeeze them out with my fingernails. That did reduce them slightly, but after a day or two, the skin would peel off like dead skin. Then, my skin would look a bit darker, and the blackheads would just come back exactly as they were. After that, I bought and tried blackhead removal products advertised online, but they didn't really work. Now that I'm older and it's a hassle, I just leave them alone, but it makes me upset every time I look in the mirror. Is there a way to get rid of them fundamentally?