Interesting. Did it have any effect on you while you were awake? Are you a lip biter?
It just seems that people who bite their lips as a nervous habit might benefit from an anti-anxiety med. It could also be appropriate for those who are having severe social anxiety as a result of their lip condition.
Stress management in general is a major factor in managing eczema & it's related conditions. Regular exercise, meditation, good diet & proper amounts of sleep... commit to it even if your lips aren't magically cured. It certainly won't make them worse, and as your lip related stress goes down you might be surprised to find they are getting better.
If not there's always Paxil, Lexapro, Wellbutrin, etc... I'm kidding, kinda. Sometimes you have to try several before you find the one that works.