One time when I asked my dermatologist for the name of a good skin cream, he recommended Curel, Cera Ve , and "if those don't work, Vaseline." So apparently Vaseline isn't bad for the skin or anything. I don't know anything about "baby formula" Vaseline; he was just suggesting regular Vaseline. It might be that you are washing with soaps your skin doesn't agree with, as well. Try something olive-oil based.
I think that this is a question for the person who is doing your hair removal. I wouldn't put vaseline on my face, personally, but I don't know how dry your face is.
I also don't know if the Vaseline would block the hair follicles from healing.
Dry skin is to be expected, but since yours is so severe, give your office a call. They can tell you what you should use. Never hesitate to call your providers with questions.
"Some people also warn against applying Vaseline to your scalp or face, claiming that it can create a breeding ground for bacteria or even block hair follicles. But there’s no evidence to back up these claims, either."
So if Vaseline soothes your dry skin and other products don't, along with trying a different soap that is oil based, I'd say it doesn't sound like there is anything wrong with using Vaseline.