im only 21 but my 34g breasts are making me miserable. Will insurance cover a reduction?

Your age should not prevent you from being able to get insurance coverage. It will just depend upon your history, documentation, and your particular insurance policy. You can start by calling your insurance company or looking up their particular policy details online. If you have been having back and/or neck pain and have attempted to relieve this pain without success with the advice or assistance of another physican, you will likely be able to obtain insurance coverage. Your particular policy will determine if you have a deductible, copay, or both. You can then have a consultation with a plastic surgeon who can help you submit your claim to the insurance company. 

Insurance
companies authorize breast reductions based on 2 criteria. One, you must have symptoms related to the
large breasts such as neck, back and shoulder pain. Two, you must meet a weight removal requirement. At size 34 each 100 grams of tissue
corresponds to 1 cup size change.
Insurance companies frequently require a minimum of 500 grams
removal. That would take you down 5 cup
sizes from a G to a B. This will be too
small for you and be disproportionate to your body. If insurance will not cover the reduction,
you will have to pay for it yourself and the cost is $10,000.Best Wishes,Gary Horndeski, M.D.

Insurance will cover most of the time if you have clinical history documented . Rashes under your breast, shoulder strapping, back pain/neck pain . All documented by your primary care . Some attempt at conservative management , such as creams for the rash, workup for back pain etc. Then the amount that is taken off in the reduction has to be enough to deem it not cosmetic surgery . That will be based on physical exam and total body surface area . This data will guestimate what needs to be taken off . All of this takes about a month. Start there then discuss cosmetic / cash and cost after it has been denied by insurance . You seem like a good candidate for a breast reduction , but an exam would be necessary to confirm that .Good Luck.

I'm sorry to hear about the physical (and probable) psychosocial problems your disproportionately large breasts have caused. 
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 psychosocial) 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 patient (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.

Your insurance requirements should be posted on the carrier's website.  Most require conservative medical management including physical therapy or chiropractic for at least six months, spinal X-rays and an orthopedic exam. Some use body mass indices to deny patients so having weight under control is important. See a board certified plastic surgeon who is knowledgeable on the insurance standards.

From your photo it is obviou you would benefit in a major way from a breast reduction procedure. As to whether or not your insurance would cover it, the only way is to see a surgeon for an exam and then the surgeon's office will contact the carrier to see if your size fits their requirements. But from the photo it is hard to imagine they would decline you.