Hi Rachel,
Are you disappointed with all the answers saying 'No' for hiring a developer with no degree? Thats fine. Anyone in your place would get disappointed with such answers.
However my answer to this question is - YES! I will not hesitate to hire a developer without a degree in my company. We are a small to medium scale company with a team size of 10+ developers. I have some developers in my team who are yet to complete their graduation degree but have an excellent coding abilities and best logical skills. They do the assigned work properly, systematically and with minimal or without error. They are a group of young and dynamic college students (just like you) who work with us mostly to earn for their studies and household income. I have observed that the amount of energy and dedication these youngsters put in the work is really awesome. They always try to learn new things and implement in their project. Technically too they are as sound as some graduate counterpart.
My point here is as a small to medium scale business owner I would definitely not hesitate to hire a developer with no degree provided he is technically sound and is dedicated to his/ her work. I am sure you possess all these qualities!
However if you want to make career with MNC's and big companies then they will surely judge you on the basis of your educational achievements. That is absolutely correct and there is no wrong in that. If you want to join any such big company in future then DO consider joining any degree or diploma course in correspondence. It will always prove to be useful to you in future.
At your age and with the technical knowledge that you have, I would recommend you to consider developing your own business of web development and not to look at others who have higher educational achievements just to get demoralized!
And I have a small disclaimer here for all those who happen to disagree with me: These are purely my own views and are based upon my own experiences in this industry since past 10 years. You are still free to and have a full right to be disagreed with my views.:)
So Rachel, how do you feel now? Spirited? Energized? Thats cool...hope my answer will help you in some way. All the best.