I'm sure you've heard of the proverb:
An ounce of prevention is worth a pound of cure.
Well, this is an example that really illustrates it. Butt burn is 1000% easier to prevent than treat, so DO NOT wait for the hospital to prescribe something! Bring your own diaper rash barrier cream when you go to the hospital and begin using it before your first bowel movement. I didn't and wound up with a terrible rash/fungal infection. The only thing good about it was that it distracted me from my incisional pain.
Butt burn is not inevitable, but it is extremely common. After a few months I did not need to use a barrier cream.
But, yeah, I don't think you have to have any particular ointment and most fit for a baby's butt are good for you too. An ingredient that is common to most is zinc oxide. No need to make this overly complex.