I'm sorry you've suffered so long. I had it for about 10 months and couldn't get it to go away... was during the summer then winter. Finally I decided to stop eating wheat and gluten. It took about 3-7 days to clear up completely and I did nothing more. However... I can't go back to wheat. The health problems it causes when I do now go way beyond cheilitis.
I feel badly that you've suffered for so long and had to share that with you. My dentist thought it was nonsense, but I recently spoke with a doctor who thinks I have celiac, even though I probably can't get a positive test.
I think it's the vitamin deficiency that would be causing the sores in the case of celiac caused cheilitis. I've always taken a B supplement and had a good diet, but when the bowel is not functioning properly nutrients and vitamins cannot be absorbed.