I don't know much about this part of it, and hospital procedures differ, but someone knows who to call. There's a venom bank somewhere in Ga that handles local species. Otherwise the Miami-Dade venom bank is probably the closest place I know of to you. There's one in texas and one in central Ca that I know about too.
Thing is, even working in an ER, you can't just call and request antivenom. You have to be an administrator type. And the hospitals in Ky may already have a procedure, where it's all banked at a specific hospital and care-flighted to others as needed.
And like you said, being an urban hospital you may not have much need for it. You probably have a protocol for getting it from somewhere that keeps it, but it's been so long since you've needed it that they don't bother to tell the staff about it as part of the standard routine.