Once you open sores on your lips, foods you eat gets directly into your blood stream, and that is the easiest way to develop new allergies.
That is the most common way how people with eczema develop allergies to topical treatments.
The same may happen with toothpaste, or anything else you put on your lips (shampoo, soap, lotions, drinks, ).
Find out what you are allergic to, or what you are intolerant of. It may be a way to solve your EC.
To deal with anxiety, do some EFT tapping. It is about 80% effective for anxiety, if you do it 10 min a day.