Try the "peeling lips forum" here at curezone... maybe there will be some info in there?
I did read in the Oil swishing forum that someone got rid of their dry lips right away, and I noticed too that though I did not have a problem with my lips, the oil swishing did make my lips very soft and supple.
However, you may have to look further for a cure for the fungal infection - maybe post to Owen, he may just have an answer for you....