Would that be okay to use together a face wash and moisturiser both containing salicylic acid?

Not a good idea: Try it with the face wash first for several weeks It may cause some irritation at first and your skin needs to become tolerant of it, which can take a month or 2. It may work fine by then and you won't need more. If you don't improve with it, I would see a doc then, and see if an antibiotic for acne would be a better next step than increasing the salicylic acid.