Have you tried an antifungal cream? There are normally fungus organisms on the skin all the time, and sometimes they become invasive and when that happens it is called tinea veriscolor.

The most common drug used is clotrimazole liquid. (You might have to have this special ordered, since commonly they don't sell it on the shelf anymore). Use it once a day on clean dry skin for about a week. Some people use RX selsun lotion (it provides sulfur, which kills the fungus, but that may be harsh on the face).

Another fungal candidate is Candida. This may become common if you take immune suppressing drugs, or are also diabetic.

Typically herpes rashes go away within 10 days, unless the immune system is wonkey. Herpes sores may be crusty. The fungal type don't get crusty.

There is another thing it could be...but your doctor would have noticed it: impetigo. This is a skin staph infection, and if you have that dreaded mrsa exposure, you need to be aggressive with it. Clean the area with hydrogen peroxide and try bacitracin ointment. If it clears
up some, keep it up. I'd get it cultured to be sure. Around the nose is normally where it shows up.