The truth is, that most web programming could be accomplished by a high school kid with the interest, some practice, and the discipline to see the job through to completion. You probably aren't ready to be the project leader just yet, but you sound like you could be a contributor. As to proving yourself, it won't be easy. Neither professional programmers nor managers, nor HR people will be ready to believe a kid can do the job. You might offer to do some work for free to get your foot in the door. Also look for an "internship", which amounts to the same thing. Remember to keep an eye on your hat size as you display and develop your mad skilzz. Expect skepticism, and don't become discouraged.