I am 19 years old, 5"3, 135lbs, and have 32DD breasts. For the longest times I have had back pain, neck pain, etc etc.

Thank you for the question. Based on your description, you may be a good candidate for breast reduction surgery. “Official” recommendations of course would necessitate in-person consultation.
Breast reduction surgery is one of the most patient pleasing operations we perform. By removing “excess” breast tissue, adipose tissue, and breast skin  this operation reduces AND lifts the breasts to a higher position on the chest wall (in other words, the breasts are "automatically" lifted when a breast reduction is performed). By doing so, patients often find improvement in neck, back, and shoulder discomfort and find it easier to form their activities of daily living and exercise.
Timing of the operation will depend on the patient's life circumstances. 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. Ask to see lots of examples of their work and communicate your goals clearly. Best NOT  to communicate your goals in terms of achieving a specific cup size; this type of communication can be a source of miscommunication. In my practice, I prefer the use's is in mof goal pictures during this communication phase;  many patients wish to remove enough breast tissue to improve/alleviate symptoms while maintaining upper/lower body proportionality.

I hope this, and the attached link (dedicated to breast reduction surgery concerns), helps. Best wishes.

It sounds like you should see a plastic surgeon for an evaluation and discuss breast reduction. Check with your insurance company to see what is needed to get it covered. See link below for more information. 

Breast reduction patients are some of the happiest patients because they get relief from their back and neck pain after surgery and look better also. Not only will you have much better quality of life, but your breast shape and proportionality will also improve. Most insurance companies do provide coverage for breast reductions based on certain standard criteria. From your description of your symptoms and your breast size you are likely a candidate. The best way to confirm your choice is to have a consultation with a board certified plastic surgeon who can help you through the process including insurance coverage.