Ron,
It sounds to me that you may have a common fungal infection that occurs in the corners of the mouth called, "angular chelitis".
It is caused by the same fungus that causes thrush inside the mouth, "candida albicans".
There are two options to treat this and both work very well on there own and can be used together in stubborn cases. Diflucan (a pill form antifungal) usually taken in one dose but, in skin lesions may be prescribed once a day for five days. Nystatin skin cream applied three times a day for up to seven days.
Dry air is actually good for helping to resolve this as fungal infections like moist areas.
This can be a real bothersome condition if not treated but, is very easy to rectify. Ask your doc about it and see if they'll prescribe you one or both of the above.
Contact me if you have any questions.
Cheers,
Mike