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I graduated college several years ago with a degree in English, and have been working in various creative positions in marketing departments since then. My current job is a kind of catch-all web content position--on a weekly basis I do everything from writing copy to making graphics to writing HTML and CSS for web pages, and design tasks have turned out to be my favorite work. Recently, my boss asked for navigational icons for the site, so I taught myself to use Illustrator and made a set of icons of which I am very proud. I am excited by all the design-related skills I've been picking up on the job, and I'd love to pursue a more focused graphic design career going forward.
My question is this: do I need a degree in graphic design to be considered for positions in this field? I feel confident in my ability to put together a portfolio and communicate the value of my experience to employers, but I'm worried that hiring managers will discard my applications without looking when they see that I don't have any kind of art degree or education. At the same time, I would much rather be working and learning on the job than accumulating student debt at this point in my life. If any of you have experience or suggestions for what direction I should pursue, I would appreciate the wisdom!