These days, the word in the fitness circuit is that you can exercise teens- not to the same degree as adults, but you can take them anaerobic through a carefully supervised program.
First, I would say you should see your pediatrician to ensure that your growth is proceeding normally. Then I would suggest getting a referral for a good coach in your area that can take you through a safely perscribed fitness program. You can find a coach here: http://www.bicyclecoach.com/
. They have an agreement with USA Cycling to provide licensed coaches to individuals and groups that are looking for a certified coach through USA Cycling. They should be able to help you.
Find a coach that will put together a training program for you for the coming season. You only need one session for this if you're just looking for a program and are dilligent with maintaining their schedule down to the letter. If you stay disiplined, you should be ok. If you think you will need more help than this, you'll need to consult your parents for figuring out how to pay for a coach.
For cycling (at least from the viewpoint of USA Cycling), the time to start becoming serious about cycling for males is now... slightly younger for the girls, since girls seem to hit puberty sooner than boys. In order to reach your fullest potential, I would highly suggest hiring a coach off USA Cycling, and let them guide you through your cycling career. They can also acquaint you with the USA Cycling circuit and the rules and guidelines of USA Cycling, as well as enroll you in the correct races and such. They can also get you discounts on your cycling gear, as well as acquaint you with the races in your area.