Dear renie: From what you describe, you may be referring to a breast ridge. Breast ridges is a description of how a breast feels. Often, at the base of the breast, there is a ridge of fat that results from gravity. If this is what you are feeling, it is nothing to worry about. If you are concerned, bring it to the attention of your doctor.
It's really impossible to evaluate a lump online. The fact that you feel something on each side, and the location you describe suggest that it's the joint between rib and cartilage and not a problem. But any newly discovered lump needs an evaluation, and that can only be done in person, with your doctor.