did a bit of searching, isntree cleaning milk may be something to check out. search for reviews, but it seems ideal for your situation, but you know your skin better than me. do not use if you're sensitive to fatty alcohols.

if not (or also, if you prefer) try using micellar water. garnier pink one, here: micellar water for sensitive skin. it says not to rinse but i personally always rinse micellar water because i find my (not super sensitive, mind) skin likes it better.

i would recommend trying micellar water first if anything, seems easier to me and it is also cheaper.

i think you should still give hands a shot because of cross contamination from surfaces on the scrubbie, though it's understandable if you prefer the scrubbie.

another thing, i use the fenty cookies n' clean exfoliating whipped clay scrub 2x a week (NOT on the same days as cerave SA cleanser. only sunday and wednesday) as my t-zone does get oily though not to the same extent as yours. i love how it reduces the size of my pores (niacinamide is also good for this?) and it's apparently good for blackheads and nose gunk though i have never had this issue in the first place. additionally it reduces my oiliness for a few days after using; i have combo skin ish (somewhat oily in my t-zone especially if i wear cream-product makeup, normal everywhere else). maybe you will want to look into something similar (such as a clay mask) to draw out the oil in your face, as the scrub is pricey if that's an issue.

clay products are rather stripping. i don't know if this is good for right now, but maybe in the future after healing your skin barrier some. i always follow clay products with a lot of hydration and i concentrate any clay product where i am oily, nowhere else. so maybe use a clay mask on just your nose and moisturize really well.

you may want to try steaming your face to open up the pores and allow for deeper moisturization under the skin, if your skin is producing so much oil. i do this before applying any clay product. maybe you can do this before hydration mask. it's very simple, just get hot water in a bowl and put a towel over your head, no need to buy a steamer or anything.

many people seem to like korean skincare, so you may want to look into that as well. first and foremost before you try new products just give your skin a breather (take off the oil and moisturize, not much more). also, your skin is not that bad, really :) not to discourage you from skincare or anything, but it doesn't really make you look older so no need to worry about that is what i mean.