I've had peeling lips for five years and during that time I had numerous blood tests which tested the standard way to test for iron deficiency-hemoglobin. All of my past tests for hemoglobin levels have been NORMAL, even on my current test my hemoglobin is NORMAL but my iron storage level (my Ferritin level) is extremely LOW.
Most doctors only check hemoglobin and if its normal they will ASSUME that you are not iron deficient. You can have enough hemoglobin but if you are low on stored iron (ferritin) then your body is deficient in iron and only has so much iron to work with, thus wound healing could be low, energy could be low etc. Some people dont have extreme symptoms when their ferritin in low.
Low ferritin is often referred to as "iron depletion".