Hello and welcome to HCM, I read your query and understood your concern. You seem to having angular cheilitis, inflammation of corners of mouth with secondary bacterial infection. It could be due to a lot of causes like dry lips due to cold, drooling, nutritional deficiency etc. Take vitamin B complex supplements. Apply topical antibiotics and steroid combination like fusidic acid /neomycin / mupirocin with hydrocortisone or beclomethasone. Keep the area well moisturized. For pain, take oral anti inflammatory like ibuprofen or paracetamol. Hope I helped.