Dude! Be careful with that 10000 IU Vitamin E oil. It's crazy strong. I strongly suggest getting something else. Hemp seed oil for one is a thing. DLD and many other advocate by vaseline.
I actually have that Vitamin E oil in 10000 IU strength. While it is good, it is really strong and only for short period of times, in my opinion. Makes the skin renew by shedding, at least in my case it did, causing a lot of discomfort. (Longer time ago, now I know the properties better and use it only when needed and in really small quantity.)
Well, we are individuals in the end, but lately I've been trying to go for products that are non-comedogenic. (Won't clog pores.) The hemp seed oil is one of those, although high in fat content.
Be safe! And I hope you get a replacement pump soon enough!