Is it by chance chapped lips or "lip-licker's dermatitis"? I had a friend growing up that had a bad habit of licking his lips, and not just his lips but all around his mouth. His face, just on the outer side of his lips would look like what you've described. This is called lip-licker's dermatitis.
From http://www.mothernature.com/Library/Bookshelf/Books/47/31...
""Chapped lips are a dehydration problem," according to Dr. Basler. "When you lick them, you momentarily apply moisture, which then evaporates and leaves your lips feeling drier than before. Besides, saliva contains digestive enzymes. Granted they're not very strong, but they don't do your sore lips any good."
"Licking chapped lips can lead to something called lip-licker's dermatitis," cautions Dr. Bark. "It's usually seen in kids but can occur in adults, too." What happens when you lick your lips is that you scrape off any oil that might be on them from surrounding areas. (The lips themselves don't have any oil glands.) Pretty soon, you're licking not just the lips but the area around them. Eventually, you end up with a red ring of dermatitis around the mouth. The moral: Don't start licking in the first place."
Hope this helps!