LRP Effaclar H + Salicylic Acid = OK Double Cleansing? [Routine Help]

Hi 23M started to get acne this year. Antibiotics cleared my skin but it came back after I stopped. Salicylic Acid dried and irritated my skin even when used with jojoba oil or cerave moisturizer.

La Roche Posay Effaclar H Iso-Biome cleansing + moisturizing twice a day makes my skin feel much better and it will take some time to see results but I think I've been getting some small blackheads on the upper cheeks. I've been thinking if the LRP Effaclar is not cleansing aggressively enough and I should do a double cleanse at night with the old drying salicylic acid + moisturizing at the end? Or can blackheads be part of a purge with the new skincare routine and they can go away on their own?

Thank you.