I'm working as nurse and I got dark circles under eye. My face is very oily especially the T-zone.
Hi Anj, very nice to meet you and thank you for joining us!
Unfortunately, topical products cannot do much for dark circles for most people. Usually the issue is caused not by hyperpigmentation, but a combo of the bone structure and stress/ not enough sleep. In terms of cosmetic improvement, an investment in a nice illuminating concealer is a better use of money and time than "anti-dark circle" skincare.
To help with oiliness, I would recommend to add an azelaic acid product to your routine in the AM. In case you can get access to this product, it's the highest concentration (it's a good thing with azelaic acid) and the best price: https://whatsinmyjar.com/product/skinoren-cream. Otherwise, something like this is a good option too: https://whatsinmyjar.com/product/naturium-azelaic-topical-acid-10 or https://whatsinmyjar.com/product/inkey-list-azelaic-acid-serum.
You could also consider adding a retinoid serum in the PM - starting from 3 times a week / every other day and then slowly increasing to daily. For example, something like this could work well: https://whatsinmyjar.com/product/indeed-labs-retinol-reface-retinol-skin-resurfacer