It can be great fun at times.. You can charge quite a bit, but clients can be a real hassle. I went into college as a programming major (fluent in C++ when I was 15; 9 years ago).. After two years, I switched my major to Interactive Digital Design, and got my BA. It's great for money, but guess what? I'm now going back to school (payed for by the money I make doing web design) for a MA in Philosophy, and eventually, a Phd. in philosophy.
My suggestion is to go to 1 or 2 lower level courses and see how you like it. Look at the curriculum of the school and see if it would be sufficient to get you into a junior web design position.
I thought I was going to be the next bill gates when I was 13 working with Visual Basic.. That changed to web design, and that turned into becoming a Philosophy professor. I'm also writing a book about how I can get virtually any job I want (literally, I change jobs every 3 months, go on practice interviews to sharpen my skills, etc.) I've never been fired, but whenever I start a new job, my friends make bets regarding when I'll leave for another job just for shits & giggles. It's just a knack that I've found and perfected over the last 3 years.
My point is, you should dabble in the field a bit and see how much you like it. If you do, then go for the gusto. One or two classes shouldn't hurt you so much financially. Not one employer that I've had (14 over the past 11 months) has ever questioned or asked me to verify my BA.
Check out a few classes, or just go to
http://www.w3schools.org/ for free, and see what you like.
For me, it's been a great source of income, and a great side job for college because I get to make up my own hours.
-Lou