i dont know if you have had any medicine for this problem but according to the information you provided it seems me that you might be suffering from angular chillitis . its a deficiency disease caused by deficiency of various vitamins
or deranged liver
function or consumption of alcoholic drinks.
you should take multivitamin
capsules like EMVIT PLUS twice daily after breakfast and dinner for three weeks then once only after breakfast for two months. drink lots of water and try to change the dental paste to see if you see any relief.
if it dose 'nt help then see a dermatologist