I’m early 20s with dry/sensitive skin (slightly oily t zone too so similar to you) but I use a combination of Kiehl’s and The Ordinary along with a few others, which has transformed my skin into a normal type.
If you’re on a budget, as a cleanser I would recommend Lush Ultrabland. It’s designed not to irritate skin AT ALL, beeswax based. This will help to balance your skin - it might be dehydrated or overly cleansed, hence the simultaneous dull and oily areas so a gentle cleanser will soothe your skin. Also removes all makeup inc waterproof.
After that, you can layer TO serums to suit your needs, such as: Hylauronic Acid or Buffet (hydration and glow), the Vit C serums (brighter skin over time), glycolic acid (evens and tones skin), lactic acid (occasional use for gentle exfoliation). Obviously you don’t need these exact products- it’s just some of the products that I own as ideas but you should tailor your routine to you. You layer these light/water based first then heavy/oily products last. (I also use various Kiehl’s products but won’t mention as not cheap)
For moisturiser I also use a Kiehl’s product, but you can try TO’s (natural moisturing factors)
For SPF, I use Kiehl’s as it’s genuinely the best once that I have tried as it doesn’t ruin my skincare underneath or my makeup over by ‘pilling’. I haven’t found a drugstore one that I like, including various LRP products
With oily skin, sometimes your face produces extra oil to overcompensate for dry skin/excessive product usage to best to start off gently.