Are your lips raw and inflamed? I don't know how bad your ec is but If you leave them completely alone for a few weeks you will get those big nasty yellow crusts which might make your ec even worse. And I'm sorry to say this but leaving them alone will take over a year for the lips to completely heal. Unless you have a mild case of ec.
The best way to manage this is to constantly moisturize the lips with Aquaphor.
Yeah, I've been to dermatologists and they didn't even know about this condition.