Oops..i forgot. Is it both breasts? (I can't remember if you said that in your post...). Is there a size difference from one breast to another?
Do you have any discoloration around the nipple area? Anything that looks out of the ordinary? Does the tissue look different?
If you have been checked by a doc (incidentally, dense breast tissue is the common way doctors describe it until you hit the perimenopausal years, don't let the term worry you) and if they found nothing, you probably don't have anything major to worry about. If you are really worried, you could insist on a mammogram. If you drink a lot of coffee or get a lot of caffeine another way, there can be breast sensitivity because of the caffeine. If your breasts are large and/or rather heavy, you might just need better support. Get professionally fitted by a trained bra saleswoman, and be sure you're in the right size and have a strong enough strap and so forth to keep the breasts from bouncing around a lot. Also, sports bras can be really useful. You wouldn't need to wear one to work or anything, but could use one for casual wear. Good luck!