Hello,
Peeling chapped skin around lips can be due to cheilitis, eczema, fungal infections or cold sores. It can be due to vit
B deficiency also. Take some
vitamin B complex for some days and see if your symptoms improve.
If the symptoms persist then please get it evaluated from a dermatologist as diagnosis has to be confirmed first.
It is very difficult to precisely confirm a diagnosis without examination and investigations and the answer is based on the medical information provided.