There's a book titled "The Acne Cure" by Terry Dubrow (one of the 2 plastic surgeons on the EV show "Botched.") [There are 91 reviews in the link about the book.]Essentially, the author says that the reason a lot of topical treatments do not work is because the acne inflammation makes the area swell, closing off the pore so that the medicine applied topically cannot get down the pore into the irritated area.
There are 3 steps to his approach and part of it is to gently apply an ice cube(s) or an ice pack to the affected area until it's chilled, blotting the water away and then applying the topical medications. It's like applying cold packs to a sprain to reduce swelling.
Maybe, your cool/cold shower is doing the same thing. If the book interests you, get it from your library and save the money for medications/treatments.
There's a book, "The Acne Cure" that might be helpful. You can request it at the library and not have to pay for it.
The basic idea of this book is that suffers should use 3 over the counter topical creams together for 6 weeks to get rid of acne. Salicylic acid, glycolic acid, then benzoyl peroxide. He also supports using ice cubes to reduce swelling before application so that the pores are not clamped shut by the swelling and the materials can get down in there.