You will find it by exploring the outskirtsIs there a way to get a shotgun or something? Or is the Hospital totally RNG? I've made it to the Mrs. Fat Zombie loads of times but have only successfully shot her once and it said she resisted the 9mm bullet. Amber one time also said to use a "Powerful Weapon".
I got excited finding the Gun Store in the Mall but it only rewards you a bunch of points and no new weapon.