I am a 16 year old girl. My breasts are size 32DDD. Is breast reduction surgery a good idea?

If you are 16 years old and your breasts are still growing then if possible you should wait until they are no longer growing for the most predictable results. Existing breast tissue can become larger after a breast reduction even if you haven't gain weight. A few of the more common reasons (besides weight gain) are use of hormones like birth control pills (even changing types) or others at the time of menopause, endocrinological problems, further normal growth if the first procedure was done at an early age, pregnancy related, and in many cases unexplained reasons. A secondary breast reduction can be performed once the cause is understood.

I'm sorry to hear about the physical and (possible) psychosocial problems your disproportionately large breasts are causing you. 
It is probable that you are dealing with juvenile breast hypertrophy along with the physical and psychosocial consequences of this diagnosis. In other words, the breasts are too large for your frame causing  both physical and (possibly) psychological distress.
In my practice, timing of breast reduction surgery is determined on a case-by-case basis. It is not too early to do your homework and learn as much as possible  about  breast reduction surgery and the potential risks and complications associated with  the procedure. I'm glad you have the support of your parents as you do your homework.
Unsatisfactory scarring is  one of the potential complications. Make sure you also understand that further surgery may be necessary in the future (for example if the breasts were to grow in size again).
On the other hand, breast reduction surgery is one of the most patient pleasing operations we perform and I think that for the right teenager (enough symptoms) it may be an excellent option (regardless of the age).
Sometimes breast  reduction surgery is covered through health insurance. The best way to obtain insurance coverage for breast reduction surgery involves some “hoops” to jump through. The more documentation you have (for example, from your primary care doctor, physical therapist, chiropractor etc.) the better when it comes to obtaining insurance “authorization” for the procedure.
This documentation and letter/pictures from your plastic surgeon will help you obtain authorization.
 When the time is right,  seek consultation with well-trained/experienced board-certified plastic surgeons.

I hope this,  and the attached link, helps.