Much like you I suffer from a similar onset of redness, which then results in drying out (casing) of the skin, which then peels away for any reason at all. For me the redness starts as sticky and sometimes burns mildly.
For a time I wondrered if it was caused from a contact allergy with a food or chemical. The prime culprit would be toothpaste or shampoo. Normal shampoos that run down your face in the shower may be enough to cause a reaction if you have a sensitivity to something in it. Personally I found this not to be a trigger, because I've trialled showering without having the lips touch the water. I've also brushed my teeth with only water (using a new brush head) for as long as two weeks at a time. I've also not brushed my teeth at all for a time.
It's of my opinion that this is not a contact irritant, because it is was, there would be more aggresive irritation and it spread over a wider surface area of the mucosa. For me the redness (see my blog) is isolated to a very small area along the lips but it has such a devestating effect on the health of my entire lips.
I've also attempted the leave alone method (without any moisturiser) and I experienced the same thing.
There seems to be a strong correlation between lip health and digestive health (both intestines + stomach). Even the dermatologist I saw many months ago suggested I come back and see him for an endoscopy/colonoscopy if the lip peeling continues. I'm currently waiting on the test.
I think it's good that you have trialled a one month leave alone because that is evidence for the dermatologist that the peeling is not caused from biting. It means you can move onto the next stage of diagnosis.
In my country I first have to see a dermatologist to get a gastroenterologist referral, so it drags out over months/years even. The sooner you start on it the better.
Candida or lip infection? Well, you can trial a steroid ointment from a dermatologist and see if it goes away. You can trial lilys epsoms salt baths and see if it goes away. You can trial more creams, you can trial different toothpastes.
Nobody though can say exactly what's happening because they don't know. It's trial and error; the more diagnostic tests you can have the better.
p.s. the photos are unclear, but perhaps the whiteness you are refering to are fordyce spots? http://mddk.com/fordyce-spots-on-lips.html
Hope this is of some use to you.