I'm 15 yrs old, 34G, 5'4, and 150 lbs. Is breast reduction a possible choice for me?

Breast reduction is possible. It really depends on your Surgeons philosophy. If you have significantly large breasts, which you may, then surgery may be an option. You must undergo significant consultation by your plastic surgeon along with your parents.  You should get several opinions.

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.

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. It is a reasonable decision -
the decision will be yours ultimately.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!