I'm 20 years old, 4'11 and 115 pounds. I am a 34G breast size. How can I get my insurance to approve this?

Thank you for your pictures.  This is not an issue.  Your insurance may cover this. It requires a bit of investigation on your part and the plastic surgeon's part.  You can definitely benefit from a breast reduction.  Start the process by seeing your primary care doc and get a referral to a plastic surgeon.

Based on the
information you’ve given, you should be able to get coverage for breast
reduction surgery. However, it will require some preparation on your part. First,
find out the specific requirements for breast reduction coverage from your
provider, as all insurance companies have different requirements. Most likely,
you will need a report from a physician linking your back pain and skin rashes
to your breast size. Some providers require patients to undergo a weight loss
program to prove that they have made other efforts to resolve their breast size
issue, but given your current body weight, I do not think that will be
necessary. You will most likely also need to have a minimum amount of tissue
removed in order for the surgery to be considered health related rather than
cosmetic related. Again, each provider is different regarding the exact amount
of tissue to be removed. Don’t hesitate to ask your breast reduction surgeon
for help in the process of getting coverage. Best of luck!

Best to call your health insurance plan to ask if you are covered for breast reduction and what are their (the plans) criteria for coverage. Than seek a boarded PS to attain a predetermination of benefits letter for you.. Good Luck. 

Thank you for the question and pictures. Based on your description and pictures, you sound like an excellent 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. 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. 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.

I hope this, and the attached link, helps.