If you have skin problems, you should really consider doing a good quality natural liver detox. The liver has over 500 functions, including dealing with fat, carbs, cholesterol, deals in part with metabolism, is the bloods filter and detoxifier... so over the years all that junk food we eat, the air pollution, the chemicals in our cleaning products and everything else overwhelm the liver, becoming toxic, which is kind of ironic since it is the main detoxifying organ. When this happens it becomes sluggish, and excess toxins can continue circulating in the blood. Another organ that detoxifies the body is the skin. You can see when someone is detoxifying their liver because sometimes this results in skin rashes, but they subside. Drinking lots of water will help the toxins pass through the urine - ensuring you have good bowel movements (2-3 a day is ideal) will help toxins leave that can't be urinated. If you detoxify your liver, make sure you are getting decent bowel movements, because if you don't, the toxins in your bowels will just get reabsorbed into the blood stream again. This is important when doing any detox. And drinking lots of water is very important, too, to keep the blood clear. When you lose weight, you detoxify from toxins that are stored in fat. They are released into the blood. So in a way, losing weight is a way of detoxifying in and of itself, and may be contributing to your skin problems.
Eating a lot of good fats and oils is essential for healthy skin and hair, not to mention brain function. I use coconut oil on my skin all the time. When I first did it, I broke out - it wasn't because of the oils (the oils in coconut oil do not clog pores anyway) - it was because it was so effective for me that it pulled all the toxins out of my skin, causing an eruption. I continued using the coconut oil to detoxify from the skin eruptions. When they subsided, I had clear, radiant skin. I also eat a diet rich in good fats, and I detox regularly. People think I'm ten years younger than my biological age.
What also helps with overall health, including your skin, liver, and so on, is your colon health - if the colon is unhealthy, your skin can reflect that. A good, natural colon cleanse (detox) might be in order. Find a natural formula that contains l-glutamine that will heal any damage in your gut - I like the cleanses by Renew Life because they contain support nutrients, healing agents (like l-glutamine), nutrients that soothe and protect the intestines and their lining. Try to find a formula that contains antimicrobial nutrients which will kill the bad bacteria. Bad bacteria produce toxins that are absorbed into your blood - so even if you eat a healthy diet, your blood can still receive way too many intestinal toxins from a previous overgrowth of bad bacteria. Then drink some kefir which contains 5 billion good bacteria (with more bacterial strains than yogurt to boot) per tablespoon, which will help colonize the colon and small intestine with good bacteria and fight off the bad guys. If your colon is not clean and functioning optimally, toxins will be absorbed into the bloodstream and make the liver work harder to detox your blood. In fact, it is the main reason our livers are sluggish and toxic in the first place. So I always encourage a colon detox before the liver detox happens.
I hope this helps!