Look up angular cheilitis, aka perlèche. There may be an antibacterial or antifungal treatment that could help you. You may also have a vitamin deficiency. Most people in this group do not have your symptoms. However, I found this interesting on the wikipedia page for AC which may apply to many of us as well:

"Allergic reactions may account for about 25-34% of cases of generalized cheilitis (i.e. not inflammation confined to the angles of the mouth). It is unknown how frequently allergic reactions are responsible for cases of angular cheilitis, but any substance capable of causing generalized allergic cheilitis may present involving the corners of the mouth alone. Examples of potential allergens include substances that may be present in some types of lipstick, toothpaste, Acne products, cosmetics, chewing gum, mouthwash, foods, dental appliances, and materials from dentures or mercury containing Amalgam fillings. It is usually impossible to tell the difference between irritant contact dermatitis and allergic contact dermatitis."

The source is this journal article which contains a big list of common allergens . . . I will be making a point of avoiding these for a while and then doing a slow reintroduction.

http://www.skinandallergynews.com/fileadmin/qhi_archive/ArticlePDF/CT/0870602...

I had this same thing recently. I got it from the super cold weather where I'm at. I did it on accident and then it got yellow crusts on them and I was freaking out. It really sucked.

Anyways, I just let them be as much as I could and tried not to open my mouth too wide but it wasn't helping much. Honestly, I was already starting to incorporate a healthier diet very slowly. Now I'm doing pretty good with diet and it just healed by itself after about a week of eating very healthy. They still bother me every once in a while but there pretty much good now.