I tried the salicylic acid face wash and it had this cooling effect that was kind of mild and intense. Is that normal?

This needs an in-person evaluation, because each skin type will have different needs. I suggest seeing a cosmetic dermatologist to get you on a long term plan with lasers, microneedling/prp, Cosmelan, peels, facials and skin care. Best, Dr. Emer.

Salicylic is an acid, so more than likely you will feel a tingling sensation. This is completely normal. Salicylic is fantastic for oily skin. It helps to regulate the oil production so I would continue to use this cleanser unless you notice some adverse reaction beyond a tingling sensation.