I don't want to sound like i'm bragging here. but i'm 19 and I have a full-time front-end developer position. although a few years back I was in the same situation you are in.
I started learning web technologies a few years ago when i was about 16 - 17, at the time i could not get enough of it, I read everything that I could get my hands on. after high-school, I knew JavaScript / HTML / CSS front to back, and was considering skipping collage and going into the work force.
At first searching for a job was hard, and my lack of experience in the field did not help at all. I worked with a lot of recruiters, although i never really got any decent offers, and the few offers I did get were for position not even related to web development.
After about a year of searching I decided to start attending some of the local developer meetups in my city. it was awesome to talk to like minded people about things I was interested in. although more importantly I was able to build up connections.
I did this for few months, and then at one of the meetups I met my future boss. we got talking about various technologies, and he mentioned they where hiring and that I should check them out. I did and that is where i am now :)
I realize that I am very lucky to have gotten such a good job so early on. although I wanted to point out that it is possible if you keep at it, and don't stop learning.
good luck :D and if you have not done so already i definitely recommend checking out some of your local dev meetups.