What can i do about extremely dry skin at the corner of my mouth?

Angular cheilitis: For starters i would suggest using a quality brand lip balm that contains sunscrean. I often see in my practice a condition called angular cheilitis. Saliva collects in the folds of skin at the corners of the mouth. Yeast colonize where it is dark and wet, and in the folds of skin, its both dark and wet, so it is actualy a fungal disease. See a dds or dermatoligist if it continues. Good luck.