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.