In my experience, using Vaseline, Aquaphor, or anything that is petroleum based, turns the skin white and actually makes it worse. The more you put on the more of the skin is 'suffocated', sometimes it even weakens the unaffected skin and then the EC spreads.
The start of EC is different to later, eventually you'll find that the build up is no longer 'thick' but you'll get to a point where its dry no matter what. Vaseline no longer turns my lip white but it doesn't help it either. I'm still trying to figure out what moisturiser is best. I've used so many now I forget what they're even called, recently I trialled Bepanthen & Eucerin, the foremost was 'okay' at moisturising but wasn't effective, the latter was useless. I'm currently using an Aloe Vera based lip balm which so far is working quite well but I don't wanna direct anyone into buying anything because odds are it won't help you until you reach the 'dry skin / no longer peeling excessively' stage.
Also peeling the skin isn't that bad as long as you can see a layer underneath, if you're peeling and its completely raw then you're halting the process. If you leave the skin on for about a week (yes, I know, a lot harder than it seems) you should see a layer underneath once you peel it. In my experience that layer looks a little better than the last and then you may be able to keep it on for a little longer before you peel, then you have more layers built up than last time, etc. Aim of the game is to restore all your layers and get to a point where the lips remain aesthetically decent enough that you don't have to peel anymore and then the inflammation can subside over whatever period of time it takes.