I know of one thing which is vitamin A-not E.
There is a very old cream made full of fish oil, but I can't remember the name of it, and I don't know if it can be found everywhere in the world so in that sense, even if I remembered its name you might not have it where you are. it is very greazy and smells awfull-fish! but it is darn good when it comes to prevent scarring and in healing pretty quick! Works 100%!
Now as I am writing this, It came back to me, it is called Ungvita!
The grandmothers used to use it because it was so good for healing, and it is still around, because it is good and works1 Not many people know it and others can't handle the smell and you only need a little any way, so the greaziness should not be a problem.
They also make one that does not smell atall for babies rashes in a tube, but that one is not very successfull, the fishy stinking one is excellent!!