I have talked with many CIO's who have gone through similar transitions in their own career. Starting as very technical and needing to transition to managing people, corporate functions and major projects. These transitions and letting go of personally being the smartest technical person in the room is often difficult. You move from your comfort zone of being very competent into a "newbie" role trying to figure it all out.
Each company is different. Your description makes it sound as though your company hasn't really thought it through very well - "just give him resources and he will figure it out". Sometimes this kind of sink or swim approach works but it could clearly end badly for you and the company.
You are no good to the company if you seriously burn out and crash. It feels like you need to push harder on the getting training and help. And, make sure your headcount lets you hire somebody in a support role that can hopefully take care of a lot of the little details of running your department.