I guess I shouldn't say that it doesn't matter at all, but it IS a myth that if you eat oily foods or chocolate that it will give you acne. If you eat junk food and have a bad diet then your skin, hair, and nails will look bad. If you eat good food then your skin and everything else will probably look healthier.
I wouldn't recommend benzoyl peroxide if you have sensitive skin. If you have sensitize skin it'll just make it worse. I had terrible skin and was using all those harsh drug store bought face washes on it, until I was told that it was irritation acne from the benzoyl peroxide. as soon as I switched to cleansers specifically for sensitive skin and got a good moisturizer it cleared right up.
I've been reading up on some natural medicine stuff, and came across some info about food intolerance. The idea is that there are some foods that your body negatively reacts to, but it is not something you are allergic to. It can contribute to things like acne, IBS, unexplained weight gain, etc. Dairy and gluten are some of the things people are most often intolerant to, and the articles I read suggested that you eliminate things from your diet for ~2 weeks, then slowly add things back in. Like add dairy in and wait awhile, then the next group and wait. If your problem cleared up in the 2 weeks or whatever time period, and it flares up again after adding a type of food back in, then you can cut that completely out of your diet. I'm sure you can find more specific information online of what foods you should cut out.