Might be sebaceous filaments rather than blackheads?

Also, try stopping dairy 100% if you haven't already.

Avoid using scrubs, brushes, exfoliating sponges, they spread blackheads more!
do gelatin peel once a week
apply nonfat buttermilk on face for 15 min, do every 2 days
raw eating cures any skin issues! Eat more fruits and veggies
drink herbal teas, they help stabilize hormones and prevent acne
honeybrush, red raspberry leaf, nettle, milk thistle
drink 30 min before meal, avoid taking with other drugs
take inside vitamin E and flaxseed oil to heal dry skin
take vitamin D3 and vitamin C,it might help with oily skin
to prevent oilyskin, wash face with cleanser once day only,and apply acne treatment once a day only
toners toocan make skin oily,not everyone needs them

Maybe you could also try this Activated Charcoal Clay Masque and Vitamin C Elixir from Banish. I see it a lot on my social media and they said that it helps with blackheads, whiteheads and oily/acne-prone skin.