Hello,
From the symptoms that you have mentioned it sounds like perioral dermatitis or angular cheilitis. Perioral dermatitis is a chronic papulopustular and eczematous facial dermatitis.It is usually characterized by an uncomfortable burning sensation around the mouth. Itching is not a common symptom.Treatment consists of oral antibiotics and anti-inflammatory drugs. A mild soap or soap substitute, such as Dove or Cetaphil should be used for washing. Scrubbing should be avoided.
If the symptoms are not controlled by topical antibiotics,then oral antibiotics may be needed.Pls consult your doctor and discuss this with them.
Hope it helps.Take care and pls do keep me posted if you have any additional queries.