16 year old 5'3 and 117 lbs with 32F (UK) saggy breasts, what are my options? (Photo)

I'm sorry to hear about the physical and psychosocial problems your disproportionately large breasts are causing. 
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 yourr frame causing  both physical and 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.   
As you learn about breast reduction surgery, make sure you read about the potential risks/complications associated with the procedure. You may find the attached link helpful in this regard.  For example, unsatisfactory scarring is  one of the potential complications. Make sure you also understands 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.

There is no doubt that you would benefit greatly from a reduction mammoplasty. Ideally when your breast size has stabilized. Did you get it done yet?

Thank you for your question! I hope that these answers help in making your decision. You suffer from juvenile hypertrophy of the breasts, which is typically treated by breast reduction. It is not uncommon to have the symptoms that you describe such as neck/back/shoulder pain as well as infections/rashes and shoulder grooving, especially in teenagers once her breasts begin to fully develop. Once one begins to have the symptoms that you state above, consideration for a surgical procedure to ameliorate your symptoms, assist with self esteem, and allow you to get back to physical activities in your youth should be done. Given your symptoms, you would be an ideal candidate. You must first discuss with your parents and pediatrician, and then consulting with a plastic surgeon for evaluation and examination to assist you in deciding if this would be the right thing for you. Your surgeon will also go over what to expect as well as the risks and benefits of the procedure. Overall, your symptoms should be ameliorated almost immediately and hopefully give you more self confidence and an increased activity level. Your breasts may still continue to grow over the next several years, but it is certainly reasonable to consider this at this age with the issues that you are having. I hope that this helps! Good luck with your decision!