So when your liver stops detoxing properly, your body will detox via other methods, which include the skin and the lungs. Some people who have general toxicity problems detox via the lungs and develop asthma, etc. Some people detox via the skin and get a variety of skin problems. It all comes down to your liver health and its not functioning optimally right now.
The alcoholism likely damaged your liver and damaged a variety of other things such as your immune system, thyroid, adrenals, etc.
If you were to get your liver enzymes tested, they likely would be elevated.
If you were to quit drinking your skin problems would likely go away. Then if you were to spend a lot of time and money and focus on cleaning up your body, then you likely wouldn’t have any re-occurring problems. It’ll take a long time, likely a few years.
Hope this helps.