oily hair

My scalp is very oily, so it still feels slippery even after washing it with shampoo. Since I have oily hair, if a shampoo is too drying, my scalp gets itchy and turns red. I also get breakouts. So, I always struggle when choosing a shampoo. I tried Dr. Groot for the first time today, and I was a bit surprised because the oiliness still lingered. If you know of any gentle products for people with oily hair like me, please recommend them.