It is true that women with large breasts are more likely to have back pain. This is because muscles in the back need to be used more in women with large breasts in order for them to maintain posture. There really isn't a particular breast size in which back pain does or does not occur. In general, they have to be significantly larger proportionally to the rest of the body (which from your description it appears yours are). Women with this problem often get breast reduction surgery
There are many other causes of back pain which are more common. For example a low back pain is often secondary to a lumbar sprain which can occur with heavy lifting. Degenerative disc disease is also common. This is when the cartilage cushion between your bony vertebrae wear down.
I suggest that you schedule an appointment with your primary care physician
. He or she can examine your back and determine whether or not your breast size could be playing a role in your pain. If it is, then you may benefit first from physical therapy. If this doesn't work, then you may look into whether or not breast reduction surgery is the right move for you.