Hi..
Welcome to HEALTHCARE MAGIC..
I have gone through your query and can understand your concern.
As per your complain the symptoms seems to be due to Exfoliative chelitis that can occur due to a number of reasons like Bacterial [staphylococcus] infection,
fungal infection,
mouth breathing,lip biting and sucking habit,
nutritional deficiency etc..
I would suggest you to apply a thick coat of petroleum jelly or bees wax containing lip balm over the lips..
Continue using neosporin..
You can apply Tacrolimus and marigold containing ointment over the lips as they seems to provide relief..
Do cool compresses over the lips..
Take
multivitamin supplements..
Avoid lip licking or sucking as it further causes dryness by evaporating moisture from lips..
Drink plenty of water..
In case of no relief in 15 days or if symptoms worsen
consult a Dermatologist and get evaluated and a thorough clinical evaluation and investigating for bacterial or fungal infection can help in deciding further course of treatment..
Hope this information helps..
Thanks and regards.
Dr.Honey Nandwani Arora.