Acne has a list of possible causes and/or aggravating factors. Eczema is very similar, and may sometimes be confused with acne. While acne can
sometimes be related to cleanliness, I don't think it is the majority cause by any means. Allergies, toxins, and nutrient deficiencies are all far more likely. In my case, eating chocolate will bring on the acne within a day or two. Eating potatoes will cause a skin rash that covers almost my entire chest. Each person will be different, and you have to figure out what your body likes and doesn't like on your own. But there are some basic principles that will be true for everyone.
There are several types of allergies. The "instant" reactions get the most press--and medical attention. Hospitals will usually test for this type using skin tests or an IgA RAST blood test. But there are other reactions that take longer to become noticeable, and which, actually, are more common/important to know about. Most doctors won't think of testing for the longer-term reaction via the IgG test, but if you can find one who does, it may be worth the money (probably around $200+ for a full foods panel test of 100+ common foods). There's a little bit of background on these several tests
HERE, but of course there is much out there if you wish to look for more.
Skin health depends on certain nutrients more than others, including vitamins A, C, E, and zinc. That last one tends to get depleted when one drains his vital essence on a daily basis, though a meat-eating diet will often provide a lot of this. For a vegetarian, pumpkin seeds and certain other foods can be good sources of zinc; or you can just use a zinc supplement. One thing to look for is white spots in fingernails. If you see some, you may need zinc.