Please read entire post as I am not advocating putting salt directly on your skin!
If your Perioral Dermatitis (PD) is caused by a fungus, it is likely growing inside your mouth (and particularly on your tongue) as well as outside your mouth. Look carefully at your tongue, especially the back of the tongue-- if it has a coating on it (the coating will change color according to what you eat-- drink a green smoothie and the coating will turn green, etc. ), then the coating is probably a fungus. You need to get rid of this fungus on your tongue.
I have found that the best way to do this is with salt and a tongue scraper (I resisted shelling out the five bucks for the scraper at first, but it works better than a spoon or a toothbrush). Take a pinch of salt and put it on your tongue and spread it around. Do this until you have covered the coating on your tongue with a little film of salt. Let it sit there for as long as you can stand it (it might start to burn a little), but ideally 5 or 10 minutes. The tongue scraper has a brush and a scraper. After the salt has been sitting on your tongue for 5 or 10 minutes, use the brush part of the scraper (or a toothbrush) to brush the entire tongue, as far back as you can. Then use the scraper part of the tongue scraper (or a spoon- but it's much easier to get the back of the tongue with a tongue scraper) and scrape the entire tongue, as far back as you can. Lots of gunk should come off. Keep brushing followed by scraping until no more gunk is coming off. Needless to say, if the tongue starts to hurt, stop and wait a day or so before trying again.
I have been doing this every night for months. At first I was doing it in the morning as well. I also try to keep my mouth as clean as possible, and brush my teeth at least twice a day.
Other remedies for killing the fungus on the skin that are listed in here are much more effective if you are also removing the fungus from the tongue. I found many helpful suggestions in here regarding diet, skin care, etc., and would suggest especially a low carb/sugar diet, lots of water, lots of leafy greens.