Congratulations on your success, and thank you for sharing with the group. Many of us have had peeling lips for much longer than you, so I think it's probable we wouldn't have as fast results as you.
I've had this for four years. I followed the anti-Candida diet for about 9 months total in 2 years and lost about 40 lbs. and drastically reduced my Candida overgrowth (tested normal but it did not cure the condition), and am now following a low-acid, organic, preservative-free, wheat- and dairy-free diet for about 6 weeks now, and have seen some improvement. Candida thrives in an acidic environment. Actually you might consider cutting out agave nectar entirely, as it slightly acidic, and substituting with raw honey (low-alkaline) or Stevia (most alkaline sweetener).
I definitely agree with you about condiments, which usually include vinegar or some preservative, which are acidic. It was also good to point out that you use Sea Salt -- which raw is alkaline, and refined is acidic. (I know people, it's maddening to keep track of it all, but honestly it's worth a shot!) Eat a ton of leafy green veggies and alkaline forming fruits, though not at the same time. Avoid tomatoes and dairy, although goat dairy is apparently alkaline. Keep eating healthy fats to stay in shape and not lose your mind (flaxseed oil, avocados, unrefined canola oil, fish oils, and coconut oil -- which is saturated fat but anti-Candida). Garlic and onions have great properties but some people's digestive systems react badly to them raw.
I definitely disagree with the popular notion with the Candida dieters that fungus are to be avoided at all costs. Shiitake, maitake, turkey tail, and chicken of the woods mushrooms all have anti-Candida properties. I think the acidity and alcohol in bread, beer, and other fermented sugary items is the issue rather than the Candida somehow feeding on yeast itself.
It would be great if you could put any pics of your lips at the height of the condition in the Image Gallery or on the wiki, with a description of how long you had it and all the other relevant allergies and topical or medicinal treatments you tried. Then update us later if the condition worsens or clears away.