barts
I went through something similar a few years ago. I didn't get a computer science degree but fell into programming on my own because I picked it up easily, but I didn't want to spend the rest of my life being a programmer and I saw that I didn't identify with other programmers that loved their jobs. I've always done some design with programming, worked around a lot of designers, and eventually switched to becoming an interaction designer (which allows me to be analytical with my work but spend a limited amount of time in code).
If there's a way for you to try something else at your current job, don't be afraid to talk to your boss and your peers about it. I thought I would get a lot of flack for not wanting to do the job I was hired for, but everyone in my company was extremely supportive. If you're a good employee, you can be as good doing something else and people want to be supportive of that (and keep you, no matter what you do).
This is something that every designer (and developer) at every media organization has to struggle with. And it speaks to what you said about someone looking in from the outside. It's very easy to create something like Andy's lovely design (and I'm sure every designer at every media organization has created or has wanted to create something similar), but it's another thing to design around all these ad sizes and push back on ad sales to have more room for creativity.