I started teaching myself HTML when I was 14 years old (I'm now 24!). I didn't do any special course or get any special qualification for it, I just kept teaching myself and learning new things. When I was around 20 years old I applied for a job as a "Junior" web designer. I didn't have any qualifications to say I can
do web design, but I did have a portfolio of the sites I'd designed. If they see that you're capable then qualifications don't matter much.
Luckily when I got the job I learnt a whole load of new things from the more experienced web designer and have learnt alot of new skills since then
So my advice to you would be to just keep learning new things, maybe finish off those sites, and create a portfolio of your work. You will then have something to show if you do go for a web design job, or even if you wanted to do freelance web design