I'd like to offer some advice as I have quite a bit of experience in the water-only method. I first tried washing with just water years ago but ultimately gave up. Why? Because it made my face red, flaky, and had minimal effects on my acne. Sometime later in the similar vein of going chemical free, I tried the caveman regimen which, simply, is the approach of not washing your face altogether. This time my face looked much clearer but the dead skin build-up deterred me from sticking with it. I mention this because it would seem that going chemical-free was an overall failure for me.
Not too long ago however I felt compelled to do more research on how to successfully use only water since I was spending too much money on useless regimens. I had hit that wall where I wanted to just say screw it. Thankfully I found a post on this site that stressed the importance of using only cold water as opposed to warm or hot, and always letting your face air dry. In my previously mentioned attempt I used warm water and dried my face with a towel each time. Apparently warmer water is inflammatory and drying, and the water pressure in the shower can be irritating. This time around though, cold water has made all the difference. I can't urge you to start washing with cold water instead as soon as possible. I began doing it by splashing my face in the sink, but dead skin was starting to slowly build-up. I suggest using a wash cloth in accompaniment to gently scrub off the dead skin and then let your face air dry. I do it before I get in the shower and then try my best to not let the warmer shower water hit my face. I do this twice a day, morning and night. That's it.
I haven't had an initial breakout or purging of any kind, only clearer and clearer skin. Also, any zits I have gotten are extremely small and heal faster than they ever have in my entire life. I've always made things worse by picking the living hell out of my skin, but now I have nothing to pick, ha. I'm seriously so pumped to actually have things under control finally. Please update if you give this a shot and notice any positive results. I'd hate to see you waste your time and see no improvement or worsen things because of something as simple, but vital, as the water temperature. Good on you for ditching the chemicals.