Like Caryopteris mentions, you may be lacking in vitamins and also minerals.
It could be a vitamin B12 or the Vitamin Bs deficiency.
You require a antifungal cream or a cream that is an antifungal and antibacterial to help and because it is on the corners of your mouth, I would suggest that you make an appointment to see your doctor so that he can prescribe the correct cream for you, the pharmacist may be able to recommend something too.
Make sure that you eat a healthy and well balanced diet. If you do have a habit of licking your lips a lot, you may need to try and stop. Don't touch your mouth with your fingers because this is how you spread germs.
Change toothpaste. Check for food issues like Celiac disease. Vitamin deficiency.