I had a million blackheads all over my nose too!
A lot of people suggest steaming and then exfoliating (2 - 3 times a week), but for me, that didn't work. But then again, this might work for you. But anyway, whether it works or not, you should still do it, because when you do, whatever cleanser you use can penetrate the blackheads more deeply, which is good, because you want to be able to cleanse them.
I've also tried those nose strips, but again, that didn't work for me, but it might work for you.
Clay masks (if you have sensitive skin, find a gentler clay mask, and maybe only put it on your nose?) a few times a week helps too. For me, when I used the clay mask, I could actually squeeze the blackheads out (usually I can't), but my nose became really red XD And yeah, most of the time, they came back... This also might work for you.
But, the thing that actually worked for me was cleansing oil. I don't know if you've heard of it but google it if you haven't. Anyway, it didn't work straight away, it took about a week or so for the blackheads to reduce, but it eventually worked, and now, I have no blackheads

Also, the cleansing oil has helped to reduce the oil production on my nose, which is good. If you're wary about cleansing oil (and putting oil on your face, or again, maybe just put it on your nose?), there are a ton of sites out there that tell you all about it. Just make sure you wash the oil completely off, or it negates the effect and could make it worse.
Finally, keep your hands away from your nose, have a good regular facial routine and try not to squeeze!