Dark spots on nose that look like sebaceous filaments, I've been BHAing and recently trying an oil cleanser with decent success but is there any way to get rid of the dark spots?

Hey all, my girlfriend noticed I have clogged pores on my nose. She used to squeeze them out, and I could see craters/empty holes where the gunk came out. I did some research and have been using Paula's Choice BHA, slowly ramping up to daily use. It wouldn't naturally remove the pores but I found if I left it on without moisturizer for an hour and then wiped it off, I would see the empty holes that I usually had to squeeze/scrape my nose to get out.

I saw another thread here recently that recommended this routine: https://fiftyshadesofsnail.com/2015/03/28/how-to-shrink-pores-temporarily-plus-3-pore-myths/comment-page-4/#comments, so I decided to try an oil cleanser as well. I've only done it for 3 days so I'm still testing things but I haven't noticed any benefits (or "felt any gunk" when rubbing it into my face after using the BHA). I feel like my pores are definitely smaller now, but I can still "squeeze stuff out" and turn the dark spots into an empty hole whereas the BHA/oil cleanser aren't doing anything. I would say my nose looks more like the second nose image in the above guide, but my spots feel much darker/pronounced if small. Are there any other ways I can 1) completely close my pores or 2) get out the last bit of sebaceous filaments?

Additionally, how should I do my routine? I used to shower+face wash and then BHA afterwards, wipe it off, and moisturize when I had the most success but with the oil cleanser it seems I should BHA > Oil Cleanser > Facewash. How can I ensure the BHA works well even if my skin may have oil+sunscreen on it from the day? Thanks :)