Possibly a dermatologist if it is a skin condition affecting the lips. If it is an infectious disease you are concerned about, then a doctor in the Infectious Diseases and tropical medicine department may be most appropriate. If you go to see your general practitioner or to a walk in centre, they should be able to point you in the best direction.
Pain in the lip can be caused by more than one kind of medical problem, however, it is probably a neurological problem which would be treated by a neurologist.
General Practitioner
what kind of doctor treats symptoms of sciaticia
Dermatologist treats that condition
I think its an orthapeadic doctor
The Dermatologist (skin doctor)
Foot doctor
An Orthopedist.
an oncologist
A psychologist.
gastroenteroligist
nuerologist
Dermatologist treats your skin diseases.
A gastroenterologist treats stomach pain.