I agree with Sam that acne can be stubborn, but the meds the doctor can prescribe now are really good compared to when I was a teenager. That's why I said that if you have had some good results with the medications or ointments, keep at it. You really have to use the stuff every day or the skin will just break out again.
Acne is a complex problem and not always easily solved. Do you have any food sensitivities? Start with analyzing what you are eating and drinking - keep a journal for an extended period of time, you may be able to see a pattern and thus eliminate the items that cause you to break out. Remember that Acne is mostly caused from what is happening on the inside of your body. Look closely, pay attention and see if you can identify the cause/s. It may take you a while, however, the journey is well worth it. Good Luck, you can do it!!
Eat as God or nature or whatever you call it and that will definitely help. FRESH food. NOTHING processed. Also, try this it worked for me as a youth: wet a towel with the hottest water you can stand and put it on your face. After a minute or so, immediately put your face in ice water for 10-15 seconds. Do this 2 x per day. Best of luck.
The real question is why you would want to do a "diet." Do you have weight issues? Food does have a big influence on most forms of acne, although which foods differ by the person. There would be a way to do any "diet" and avoid foods you want to avoid, as there are a lot of foods available in today's global economy. But fad diets like this one really haven't proven themselves to work over long periods of time, and while high protein diets are quite a fad today, they seem only to work short term for weight loss and over a long period of time can actually be harmful to your kidneys. The diet that proves out the best every time is the good old balanced diet one, which we've come to call the Mediterranean Diet, but isn't confined to that area of the world. It's a diet high in whole grains, low in red meat (which pretty much rules out all the high protein fad diets), lots of fruits and veggies (in your case you'd want to avoid too many sugary fruits), and fish. It's still the winner in the how to eat sweepstakes, at least as far as long-term studies are concerned. But if you really want to do keto, there are again a lot of different foods you could substitute to get to what they claim is a fat-burning diet, which of course doesn't actually exist but if you like it, you get to do it. Just choose foods that meet the criteria while avoiding the foods that you associate with your acne problems. Peace.
I don't know the ins and outs of the keto diet, but if you have periods of time during the day when your blood sugar is below a certain level, that would be good to reduce acne. Eating all throughout the day (which keeps your blood sugar high all the time) increases the chance of getting acne.