I've been 'the computer guy' all my life - when I was 13-15, I was volunteering at a non-profit computer repair place that ripped apart donated computers, fixed them, and gave them back to other non-profits like churches and social organizations. By the end of my time there, I was actually teaching weekly repair classes to other volunteers, often 30-50 years old.
Anyways, I'm not meaning to wank off, but when I went to college, I specifically didn't study computer science, because I was pretty secure with my tech abilities, and figured I'd always be able to find a job. I double majored in Psych and Philosophy.
After college, it was a little hard to find a job, but I don't think it had anything to do with my lack of a CS background. I just explained my choice of major at university, and spun it in a positive light. IE "The analytical skills I learned in my philosophy program are directly applicable to the type of complex problem solving needed in IT environments, and in fact give me an edge of 'outside the box' thinking over my CS major counterparts" or whatever.
After I had my first job, college began mattering less and less - employers look more at past experience. In fact, I think it matters so little that I went and quit my job for a year to get a masters in Cognitive Science. No problem finding a job when I got back, and I've since started my own small business IT company that is doing quite well. Point is, if you have the skills, you'll be fine!