Inflammation of the lips is called cheilitis. This is more common in women than men. Although colored tootpaste and mouthwash are often blamed, I have rarely found them to be at fault. Try not using mouthwash for a while, and use only white toothpaste. Meantime, have your doctor prescribe a cortisone ointment. That will almost surely clear you up.
As with any eczema, the condition may recur, requiring you to reapply the ointment from time to time.
Ask your dermatologist (perhaps a different one) whether allergy patch testing is necessary. In my experience, it rarely is. People just easily hold the condition in check with occasional use of the apporopriate cream, with or without moisturizing also.
Best.
Dr. Rockoff
Thank you. I do use Plax mouth wash every day and I also have eczema on my hand, so this seems more logical to me.