From the description that you have given.It looks like you are suffering from Cheilitis
.There are many different types of cheilitis due to different causes.It is very important to understand what is causing this before starting the treatment.Since i have not seen you.i would suggest you continue the treatment your dermatologist
has prescibed.Apart from the treatment i would suggest you not to lick your lips,keep the lips supple by washing it with cold
water and applying aquaphor lip repair
,avoid excessive exposure to sun.If there is any oozing along with chapping it could be due to infective causes contact your dermatologist.