Am 5'1 and since I was 12 my breasts started growing and now am 30J or 30JJ cup size. Should I go for surgery? (photo)

Thank you for the question. Based on your description you may be an excellent candidate for breast reduction surgery.   However, much more information is needed to determine whether you should proceed with surgery, and if so when (timing).  In my practice, I individualize the “timing” of surgery based on a lot of information that is transmitted during the consultation process.
“Typical” patients who present for breast reduction surgery are women who have disproportionately large breasts, causing problems such as neck/back/shoulder discomfort, postural changes, bra strap grooving, skin irritation/rashes under the breasts, and/or difficulty with activities of daily living and/or exercise etc. There may be both physical as well as psychosocial “stress” caused by the disproportionately large breasts.
Reducing breast tissue mass and elevating the breasts on the chest wall tend to improve or alleviate many of the symptoms associated with the disproportionately large breasts.
Patients considering breast reduction surgery should also consider the potential downsides (risks/complications) associated with the procedure as well.. Poor scarring, for example may be associated with the procedure.  Additional surgery may be necessary in the short or longer term for a multitude of reasons.
When the time is right, I would suggest starting with consultation with well experienced board-certified plastic surgeons.
Then, I would suggest you visit a few surgeons whose practices concentrate on aesthetic surgery. Ask to see lots of examples of their work and preferably speak/see patients who have had similar procedures done.
Then, it will be important that you communicate your goals clearly with your plastic surgeon and make sure that you have realistic expectations prior to proceeding with any type of surgery. In regards to breast size desired, also communicate carefully. In my practice the use of goal pictures are helpful in this regard; a discussion of cup size can be confusing and imprecise.   Therefore, I would not suggest that you communicate your goals and/or base your satisfaction with the outcome of surgery on achieving a specific cup size.  I also find that the use of pictures is more helpful than the words “natural” or "proportionate” etc., which can mean different things to different people.
Many of my patients choose to have enough breast tissue removed to help alleviate symptoms while retaining enough breast tissue to remain proportionate to the remainder of their torso.
I hope this helps.

Yes, go visit with a board-certified plastic surgeon and discuss having a breast reduction which includes a lift. It is possible that insurance might cover your surgery. Start with your medical doctor to get a referral for this.

You need a formal evaluation by a licensed plastic surgeon and expert in breast reductions to determine what is best for you and your goals.
Breast reduction is one of my favorite surgeries as it allows me to dramatically improve a woman’s breast appearance as well as alleviate many physical symptoms of large breasts, such as back, neck and shoulder pain, bra strap grooving, and rashes under the breasts. When I perform breast reduction surgery, I generally use a superomedial pedicle to provide blood supply to the nipple while maintaining fullness in the upper and inner breast. Excess lower and outer breast tissue are removed. Breasts are often asymmetrical, so I remove more tissue from the larger breast. The final scar pattern is a circle around the areola, down the breast, and possibly under the breast, depending on the degree of skin excess.
For me, breast reduction is not a one-size-fits-all surgery. The size and shape of the breasts are customized to each patient depending on her goals and desires. Some women want a significant amount of tissue removed while others prefer to have a more limited reduction. Regardless of the amount of tissue removal, I perform the maximum safe amount of lifting and tightening for each patient.
I suggest consulting with a board-certified plastic surgeon and expert in Breast Reductions. - Dr. Cohen