Hello,
It can be due to cheilitis which is of three types: simple, superficial suppurative and deep suppurative. There are dilated ductal openings on the mucosal surface of the lips which may have suppurative discharge. Confirmation is done by bacterial and fungal culture of the suppurative discharge from the lips and lip biopsy.
It is very difficult to precisely confirm a diagnosis without examination and investigations and the answer is based on the medical information provided. For exact diagnosis, you are requested to consult your doctor. I sincerely hope that helps. Take care and please do keep me posted on how you are doing.
Take B-complex vitamins! It might help!